Question

1. Express the complex number in trigonometric form.

3

2. Express the complex number in trigonometric form.

-6i

3. Express the complex number in trigonometric form.

3 - 3i

4. Find the product of z1 and z2, where z1 = 7(cos 40° + i sin 40°) and z2 = 6(cos 145° + i sin 145°).

5. Write the complex number in the form a + bi.

3(cos 270° + i sin 270°)

Any help is appreciated !!!

Answer 1

See below.

Explanation:

The trigonometric ( or polar) form of z= a+bi is z = r(cosθ+isinθ) .

So for Part 3 3 - 3i we have r = √(3^2 + (-3)^2) = 3√2 and θ= arctan(3/-3) = arctan (-1) = -π/4.

So the answer is 3√2(cos(-π/4) + isin(-π/4).

Part 1. 3 = 3(cos 0 - i sin 0).

Part 2. -6i = 6(cos (-π/2) - isin -(π/2)