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
What type of shape is the locus of points satisfying $|z - 3| = |z + i|$?
A
A half-line
B
None of the above
C
A line
D
A circle
E
Two circles
Question 2
If $z = 3 + 5i$ and $w = 2 - i$, what is $z - w$?
A
$\frac{1 +13i}{5}$
B
$11 - 7i$
C
$1 + 6i$
D
None of these
E
$5 + 4i$
Question 3
If $z = -\sqrt{3} - i$, what is $\arg(z)$?
A
2
B
$\frac{-5\pi}{6}$
C
$\frac{\sqrt{3}}{3}$
D
$\frac{\pi}{6}$
E
-2
Question 4
If $z = 3 + 5i$ and $w = 2 - i$, what is $z/w$?
A
None of these
B
$11 - 7i$
C
$1 + 6i$
D
$5 + 4i$
E
$\frac{1 +13i}{5}$
Question 5
If $z = -\sqrt{3} - i$, what is $|z|$?
A
$\frac{\pi}{6}$
B
-2
C
$\frac{-5\pi}{6}
D
$\frac{\sqrt3}3$
E
2
Question 6
What is $\sqrt{5 - 12i}$?
A
None of the above
B
$\pm 3 \mp 2i$
C
$\pm 3 \pm 2i$
D
$3 - 2i$
E
$-3 - 2i$
Question 7
If $z = 3 + 5i$ and $w = 2 - i$, what is $zw$?
A
$\frac{1 +13i}{5}$
B
None of these
C
$5 + 4i$
D
$11 + 7i$
E
$1 + 6i$
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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.