Quiz 2: Complex Numbers

Express 4(cos2π/3 + isin2π/3) in a + bi form.

-2 + 2√3i

Simplify (-1 + i)^4.

-4

Find the quotient of 6(cos150° + isin150°) and 1/2(cos15° + isin15°).

-6√2 + 6√i

If z = √2 - 2i, then |z| = _____.

√6

Which of the following is a solution of z^6 = 64i?

2(cos135° + isin135°)

Find z1z2 if z1 = 3(cos37° + isin37°) and z2 = 2/3(cos53° + isin53°).

2i

Each of the solutions of z4=81 has a modulus of ____.

3

If z = (15 + 8i) ÷ (3 - 4i), then |z| = _____.

3 2/5

The 12th roots of unity have arguments that are multiples of _____.

30°

What is the argument of 3 - 3i?

315°

Express 36i in polar form.

36(cosπ/2 + isinπ/2)

Find [2(cos15° + isin15°)]^4 and express it in a + bi form.

8 + 8√3i

Determine in which quadrant the product of 5(cos3π/8 + isin3π/8) and √2(cosπ/12 + isinπ/12) lies.

I

In which quadrant does 3(cos5π/4 + isin5π/4) lie?

III

If the argument of a complex number in polar form is 3π/2, then it lies on the _____.

negative imaginary axis