# Worksheet: Polar Form of Complex Numbers

In this worksheet, we will practice representing a complex number in polar form, calculating the modulus and argument, and using this to change the form of a complex number.

**Q12: **

Simplify , giving your answer in both algebraic and trigonometric form.

- A ,
- B ,
- C ,
- D ,

**Q19: **

Given that , determine the algebraic form of , approximating the real and imaginary parts to the nearest two decimal places.

- A
- B
- C
- D

**Q20: **

Given that , find the principal argument of , where .

- A
- B
- C
- D
- E

**Q21: **

Find .

- A
- B
- C
- D
- E

Find .

- A
- B
- C
- D
- E

Hence, express the complex number in rectangular form.

- A
- B
- C
- D
- E

**Q22: **

Given that , find .

**Q23: **

Find the modulus and the principal amplitude of the number .

- A , principal amplitude
- B , principal amplitude
- C , principal amplitude
- D , principal amplitude

**Q24: **

Find the modulus and the principal amplitude of the number .

- A , principal amplitude
- B , principal amplitude
- C , principal amplitude
- D , principal amplitude

**Q25: **

Find the modulus and the principal amplitude of the number .

- A , principal amplitude
- B , principal amplitude
- C , principal amplitude
- D , principal amplitude