# Worksheet: Operations on Complex Numbers in Polar Form

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

Q1:

Given that and , find in polar form.

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Q2:

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

• Amultiply their moduli together and add their arguments
• Badd their moduli together and multiply their arguments
• Cmultiply their moduli together and multiply their arguments
• Emultiply their moduli together and subtract their arguments

Q3:

Given that and , find .

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Q4:

What is the argument of the product of and ?

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Q5:

Given that , find .

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Q6:

Given that and , find .

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Q7:

Given that , , , and , find .

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Q8:

Given that , , and , where , find .

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Q9:

Given that and , find the exponential form of .

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Q10:

If , , and , then what is ?

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Q11:

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Q12:

Given that and , find .

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Q13:

Given that and , where , determine the trigonometric form of .

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Q14:

Given that and , determine .

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Q15:

Given that and , determine .

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Q16:

Given that and , find .

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Q17:

Given that and that , find .

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Q18:

What is the magnitude of the product of and ?

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Q19:

Given that principal argument of and principal argument of , determine the principal argument of .

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Q20:

Given that the principal argument of and the principal argument of , determine the principal argument of .

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Q21:

Given that principal argument , determine principal argument .

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Q22:

Given that and , find the trigonometric form of .

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Q23:

If , what is ?

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Q24:

Given that , find .

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Q25:

Given that , find .

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