Assessment: Complex Numbers

What is i²?

In z = a + bi, what is "b" called?

Compute (6−3i) + (−2+5i).

Find |z| for z = 5+12i.

Multiply (3+2i)(3−2i). (The result is purely real — enter just that number.)

Divide (2+6i) by (2+i).

Electrical engineers represent AC circuit impedance as a complex number. Which form makes it easiest to multiply two impedances (by simply multiplying magnitudes and adding angles)?

A signal-processing engineer needs to compute a complex number raised to the 10th power quickly. Which tool makes this direct, rather than tediously multiplying it out 10 times?

Why are the nth roots of a complex number always evenly spaced around a circle?

Simplify i¹⁰⁰ using the 4-cycle pattern of powers of i, and give the result as a real number.