In this worksheet, we will practice performing calculations with complex numbers in polar form.

**Q2: **

What do we need to do to multiply two complex numbers in polar form?

- Aadd their moduli together and multiply their arguments
- Badd their moduli together and add their arguments
- Cmultiply their moduli together and multiply their arguments
- Dmultiply their moduli together and add their arguments
- Emultiply their moduli together and subtract their arguments

**Q3: **

Given that and , find .

- A
- B
- C
- D
- E

**Q4: **

What is the argument of the product of and ?

- A
- B
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- D
- E

**Q5: **

Consider the complex number .

Find the modulus of .

Find the argument of .

- A
- B
- C
- D
- E2

Hence, use the properties of multiplication of complex numbers in polar form to find the modulus and argument of .

- Amodulus = , argument=
- Bmodulus = , argument =
- Cmodulus = 8, argument =
- Dmodulus = 8, argument =
- Emodulus = , argument =

Hence, find the value of .

**Q7: **

Given that , find .

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- C
- D

**Q8: **

Given that and , find .

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- E

**Q9: **

Given that , , , and , find .

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- D

**Q10: **

Given that , , and , where , find .

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**Q11: **

Given that and , find the exponential form of .

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- E

**Q12: **

Given that and , find , giving your answer in exponential form.

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- E

**Q17: **

Given that and , determine .

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- E

**Q18: **

If and , is it true that ?

- Ayes
- Bno

**Q19: **

Given that and , determine .

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- D
- E

**Q20: **

Given that and , find .

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- E

**Q21: **

Given that and that , find .

- A
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- D

**Q22: **

Given that , find , giving your answer in exponential form.

- A
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- D
- E

**Q25: **

If , , and , what is the exponential form of ?

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- B
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- D
- E