Complex Numbers

On this page, you can access a short multiple-choice-question exam that tests the concepts of this topic. If, instead, you want to practice the past paper questions for this topic, Click Here

There are 10 main questions in this chapter. These can be broken down into dozens of simpler questions. You will be tested by all of them. This test may be quite long. We recommend doing this test on a computer or tablet, not on a smartphone.

Do not guess any answers, you would only cheating yourself. If you think you know the answer from memory but cannot explain why it is the answer, then select the "I don't know" option. You are here to get an honest assessment of your progress, for your own benefit.

These questions cover the curriculum for this topic. This test will let you know how strong you are on this topic, if you treat it properly. Bluffing and guessing are counter-productive to your goal.

1. Simplify \((2+2i) + (3-i)\)
2. Simplify \(\frac{3-2i}{1+i}\)
3. Expess \(4-3i\) in polar form
4. Convert \(4(\cos(\frac{\pi}{3})+i\sin(\frac{\pi}{3}))\) to rectangular form
5. What is \((4-3i)^9\) ?
6. Simplify \((3-2i) \times (4+3i)\)
7. Express \(4(\cos(\frac{\pi}{2})+i\sin(\frac{\pi}{2})) \times 3(\cos(\frac{\pi}{3})+i\sin(\frac{\pi}{3}))\) as a single complex number
8. Simplify \(4i \times 3i\)
9. Solve \(z^3 = 1\), for three values of \(z\)
10. If \(z^2=4i\) what is \(z\) ?