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Who is Afraid of Big Bad "i"? Trivia Quiz

Are you a mathophobe? Afraid of all things algebraic, analytic and whatnotic? Let this quiz take you step by step and amaze your friends with your knowledge of complex numbers.

A multiple-choice quiz by triviapaul. Estimated time: 5 mins.

Author
triviapaul

Time
5 mins

Type
Multiple Choice

Quiz #
212,370

Updated
Oct 16 23

# Qns
10

Difficulty
Average

Avg Score
7 / 10

Plays
782

One at a Time - Single Page

Question 1 of 10

1. I'll start by warning all those math die-hards who want everything with mathematical precision that I am cutting corners big time so don't get upset.

Until we had complex numbers, we were quite happy with the numbers we had. These were called: Hint

Integer

Rational

Real

Counting

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Question 2 of 10

2. I hear you say "why do we need those stupid numbers". We'll come to that later, first let's talk about "how" we do them. Since all numbers were covered by the ten digits we already knew, we needed another unit. We call this unit "imaginary" and represent it by the letter "i". What does "i" stand for in terms of non-complex (real) numbers? (Hint: if you have a calculator, use it). Hint

Square root of a very very large number

Square root of 1

Square root of -1

Square root of 0

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Question 3 of 10

3. To make a complex number is easy: you just add the imaginary "i" part to the real part. Most complex numbers take the form "a real number plus an imaginary part" where the imaginary part is a couple of "i"s. Which of the following are valid complex numbers? Hint

1+i

All of these

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Question 4 of 10

4. So you see, a complex number z has a real amount called Re(z) and an imaginary amount called Im(z). Just to check if you are with me: what is the imaginary part Im(z) of 5 + 4*i Hint

4*i

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Question 5 of 10

5. Now about the why: this might sound silly to you, but complex numbers make life easier for mathematicians and are easy to work with. For example: mathematicians like smooth rules like "a polynome of degree n has n roots".
To explain this, try to figure out these two :
If x - 1 = 0, what is x
and
If x^2 (that's x squared: x*x) - 1 = 0, what is x?
(Hint: fill in the answers and see what happens) Hint

1 for the first, 1 and -1 for the second

0 for the first, 1 and 2 for the second

1 for the first, 2 for the second

0 for the first, -1 and -1 for the second

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Question 6 of 10

6. If you haven't given up by now: bravo! If you get this one right you know your complex numbers already. What is/are the solution(s), called root(s), of x^2 + 1 = 0? Hint

- 1 and - i

i and - i

1 and - 1

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Question 7 of 10

7. If you are happy that you understand it until now, you are absolutely right! If you want, you can stop now, but if you've made it this far, you might want to continue; it could be interesting to find out how to visualize a complex number.
Take a piece of paper and draw a big cross, like a big "+". from left to right we put the real part of a complex number and from bottom to top the imaginary part.
In the middle of the "+" is the 0 for both. 1 is right of the "+", - 1 is left of the "+", i is in the direction of top, - i is going down. Where do you think would 1 + i be?
Hint

Way down

Somewhere in the top right quarter

Could be anywhere

A little bit left

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Question 8 of 10

8. This is the fun part: detecting complex numbers in real life.
Take a look at a bicycle wheel. Attach something on the tyre (a piece of duct tape for example) or mark it in any other way. Now look at it from the side and give it a spin. If you imagine that the hub of your wheel is the middle of the real-line-imaginary-line cross, how would you describe the movement of your marker? Hint

It makes circles around the middle

All of these

It goes left and right through the real part

It goes up and down through the imaginary part

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Question 9 of 10

9. Again put a marker on the rim of the bicycle wheel and give it another spin. If you look at the same wheel from above now (so that you only see the tyre but not the spokes), what kind of movement is your marker making? Hint

It doesn't move

Up and down in a jumping kind of motion

Left to right and back in a wave - like motion

Still making circles

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Question 10 of 10

10. If you never heard of complex numbers before but had no problems with this quiz, you have missed your calling. Please report to the next engineering school immediately.

For extra credit, especially those mathematicians who were getting really bored. In my field, electrical engineering, we don't use "i" but "j". Why is that? Hint

The founder of modern electrical engineering, Julius Cesar Maxwell, mistakenly used "j" and it stuck

the "i" was invented by mathematicians and we are an envious lot

In an important formula in electrical engineering using the "i" would make a dirty word

We use the "i" already for something else and don't want to be confused

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Quiz Answer Key and Fun Facts

1. I'll start by warning all those math die-hards who want everything with mathematical precision that I am cutting corners big time so don't get upset. Until we had complex numbers, we were quite happy with the numbers we had. These were called:

Answer: Real

In the beginning we were just counting 1, 2, 3, and were happy. We called them counting or natural numbers. Then the Indians invented chess and the zero and people soon found out that you could actually count backward from zero thus inventing negative numbers. We called the whole bunch Integers and we were happy.

Then someone had to divide three apple pies between eleven children and had to invent fractions (you know... numerator, denominator).These numbers still made sense, right? So we called them Rational.

Then mathematicians started to emerge and he was not satisfied, he invented pi and e and sqrt2 : stuff you can't write as a fraction. In the true spirit of their predecessors mathematicians called these numbers irrational, put his arms around all numbers known and called them "real". And we were happy. (Actually the historical order of invention is: rational, irrational, zero, negative... I told you I was cutting corners).

Answer: Square root of -1

Try it on your calculator: sqrt of 0 will give you 0, sqrt of 1 will give you 1 but sqrt of -1 will give you an error. The only way "i" is really defined is by saying i times i is -1 (i*i = -1).

Answer: All of these

A little bit of a stinker, really. "i" is the same as 0 + i and 1 is the same as 1 + 0*i. So they are all complex and all real numbers are also complex.

4. So you see, a complex number z has a real amount called Re(z) and an imaginary amount called Im(z). Just to check if you are with me: what is the imaginary part Im(z) of 5 + 4*i

Answer: 4

Just to clarify: the imaginary part are all the "i"s not just the letter "i". real part: 5, imaginary part: 4

5. Now about the why: this might sound silly to you, but complex numbers make life easier for mathematicians and are easy to work with. For example: mathematicians like smooth rules like "a polynome of degree n has n roots". To explain this, try to figure out these two : If x - 1 = 0, what is x and If x^2 (that's x squared: x*x) - 1 = 0, what is x? (Hint: fill in the answers and see what happens)

Answer: 1 for the first, 1 and -1 for the second

Below you see already a lot of x's, don't be alarmed, the explanation is easier than it looks and if you have this question right without guessing, you might have some hidden talents.
You see that it works only for the one solution x = 1, we say that 1 is the root. x - 1 = 0 is called a polynome of degree one, for it has only an "x".
x^2 - 1 = has two solutions, two roots: it works if x = 1 and if x = -1. It is degree 2 because it has a "x^2".
The "degree" of a polynome is defined by the "highest x". So x^2 + x + 1 = 0 is also degree 2. x^3 + x^2 + x + 1 = 0 would be degree three and has, you guessed it, three roots.

6. If you haven't given up by now: bravo! If you get this one right you know your complex numbers already. What is/are the solution(s), called root(s), of x^2 + 1 = 0?

Answer: i and - i

Just fill it in: for x^2 + 1 to be 0, x^2 has to be -1. That is exactly the definition of i. Note that this is a degree 2 polynome with 2 solutions and that -i*-i is also -1.

7. If you are happy that you understand it until now, you are absolutely right! If you want, you can stop now, but if you've made it this far, you might want to continue; it could be interesting to find out how to visualize a complex number. Take a piece of paper and draw a big cross, like a big "+". from left to right we put the real part of a complex number and from bottom to top the imaginary part. In the middle of the "+" is the 0 for both. 1 is right of the "+", - 1 is left of the "+", i is in the direction of top, - i is going down. Where do you think would 1 + i be?

Answer: Somewhere in the top right quarter

It's quite straightforward, really. 1 is to the right, i is going up, therefore 1 + i is top right. Top left is the - 1 + i part, bottom left is - 1 - i and bottom right is 1 - i. Draw it out on your piece of paper and you will see it makes sense.

8. This is the fun part: detecting complex numbers in real life. Take a look at a bicycle wheel. Attach something on the tyre (a piece of duct tape for example) or mark it in any other way. Now look at it from the side and give it a spin. If you imagine that the hub of your wheel is the middle of the real-line-imaginary-line cross, how would you describe the movement of your marker?

Answer: All of these

Your marker will make circles around the hub, and it goes through all quarters in order, crossing the real and imaginary axis on its way.

Answer: Left to right and back in a wave - like motion

When you look from above, you don't see the circle of the wheel anymore, you just see a line and your marker is moving on it like a wave. What you see is the real part of a complex number! The line relates to the wheel as the real number relates to the complex number.

The wave you see is called a sine wave, maybe you heard of it. Similarly, when you look at the wheel from the front, you see the same wave (it just starts from a different point, it's called a cosine wave).

10. If you never heard of complex numbers before but had no problems with this quiz, you have missed your calling. Please report to the next engineering school immediately. For extra credit, especially those mathematicians who were getting really bored. In my field, electrical engineering, we don't use "i" but "j". Why is that?

Answer: We use the "i" already for something else and don't want to be confused

In electrical engineering the "i" is used as the symbol for electrical current, obviously quite an important property. So important we don't want to use it for anything else.
J.C Maxwell's first names are James Clerk. His laws are the foundation of electromagnetism.
Our formulas use symbols which are too extravagant to be offensive, but if the situation arises, we can always put the symbols in a different order. (If someone knows of offensive formulas please tell me... that would be excellent trivia).
Personally I am not envious but very thankful to the mathematician community; every time it gets too difficult for us (the same goes for physicists) we turn to them to help us out.

Source: Author triviapaul

This quiz was reviewed by FunTrivia editor crisw before going online.
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