This precalculus complex polar quiz asks 10 multiple-choice questions on complex numbers in polar form, and each answer comes with a short explanation.
Ten multiple-choice questions on complex numbers in polar form: modulus and argument, conjugates, polar conversion, products, De Moivre’s theorem, distance and midpoint. Choose the one best answer, then read the explanation to learn which mistake each wrong option comes from.
Use De Moivre's theorem to evaluate \((1-i)^{6}\).
A\(8i\)
B\(-8i\)
C\(8\)
D\(-8\)
Question 8
What is the distance between the two complex numbers shown?Two complex numbers.
A\(7\)
B\(25\)
C\(1\)
D\(5\)
Question 9
Find the midpoint of \(-4+i\) and \(6+5i\).
A\(2+6i\)
B\(5+2i\)
C\(-5-2i\)
D\(1+3i\)
Question 10
The figure shows \(3+i\). Which number is \(i(3+i)\), the point rotated \(90^{\circ}\) counterclockwise?The point 3 + i and a rotated point.
A\(1-3i\)
B\(-1+3i\)
C\(-1-3i\)
D\(1+3i\)
🎉 Quiz complete!
0 / 10
How does this quiz work?
Read each question, choose one answer among A, B, C and D, then check it: a short explanation appears after every answer. Your score out of 10 is shown at the end, and you can restart the quiz as often as you like.
What should you review before the quiz?
Reread the key facts of the lesson and the worked example. If a question is hard, go back to the matching part of the lesson, then try the quiz again. Write your work on scrap paper: most mistakes come from skipping a step, not from the idea itself.
Remember:
Modulus |a + bi| = √(a² + b²); the conjugate a − bi satisfies z · z̄ = |z|².
Polar form: z = r(cos θ + i sin θ), with a = r cos θ and b = r sin θ.
