Doing Further Maths? Feeling a bit left out by all of these other, non-FP1 quizzes? Well, let me put that slightly right. Here are a few questions on complex numbers for you.

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Question 1

If $z = 3 + 5i$ and $w = 2 - i$, what is $z/w$?

A

$11 - 7i$

B

$1 + 6i$

C

$5 + 4i$

D

None of these

E

$\frac{1 +13i}{5}$

Question 2

If $z = 3 + 5i$ and $w = 2 - i$, what is $zw$?

A

$5 + 4i$

B

$1 + 6i$

C

$\frac{1 +13i}{5}$

D

$11 + 7i$

E

None of these

Question 3

What is $\sqrt{5 - 12i}$?

A

$\pm 3 \mp 2i$

B

$\pm 3 \pm 2i$

C

None of the above

D

$3 - 2i$

E

$-3 - 2i$

Question 4

If $z = 3 + 5i$ and $w = 2 - i$, what is $z - w$?

A

None of these

B

$1 + 6i$

C

$11 - 7i$

D

$5 + 4i$

E

$\frac{1 +13i}{5}$

Question 5

What type of shape is the locus of points satisfying $|z - 3| = |z + i|$?

A

None of the above

B

A line

C

Two circles

D

A circle

E

A half-line

Question 6

If $z = -\sqrt{3} - i$, what is $\arg(z)$?

A

$\frac{-5\pi}{6}$

B

2

C

$\frac{\pi}{6}$

D

$\frac{\sqrt{3}}{3}$

E

-2

Question 7

If $z = -\sqrt{3} - i$, what is $|z|$?

A

$\frac{\sqrt3}3$

B

2

C

$\frac{-5\pi}{6}

D

-2

E

$\frac{\pi}{6}$

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Colin

Colin is a Weymouth maths tutor, author of several Maths For Dummies books and A-level maths guides. He started Flying Colours Maths in 2008.
He lives with an espresso pot and nothing to prove.

## MathbloggingAll

FP1 Complex Numbers quiz http://t.co/6mwk1dEKov

## Joshua Zucker

You have a typo in one of your questions: it should be (1+13i)/5, not /3.

## Colin

Thanks! Have put it right, I hope!

## Joe

The answer to question 1 is slightly wrong. It should be [correct answer], as opposed to [wrong answer]. Hope this helps.

## Colin

Thanks, Joe, you’re quite right! I’ve fixed that now.