Lesson Worksheet: Operations on Complex Numbers in Polar Form

Q1:

Given that and , find in polar form.

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D
E

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
Dadd their moduli together and add their arguments
Emultiply their moduli together and subtract their arguments

Q3:

Given that and , find .

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E

Q4:

What is the argument of the product of and ?

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E

Q5:

Given that , find .

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D

Q6:

Given that and , find .

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Q7:

Given that , , , and , find .

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Q8:

Given that , , and , where , express in trigonometric form.

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Q9:

If , , and , then what is ?

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D112

Q10:

Simplify , giving your answer in trigonometric form.

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D

Q11:

Given that and , find .

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Q12:

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

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E

Q13:

Given that and , determine .

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E

Q14:

Given that and , determine .

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E

Q15:

Given that and , find .

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E

Q16:

Given that and that , find .

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D

Q17:

What is the magnitude of the product of and ?

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E

Q18:

Given that and , find the trigonometric form of .

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D

Q19:

If , what is ?

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Q20:

Given that , find .

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Q21:

Given that , where is an integer, find .

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Q22:

Given that and , where and , find , giving your answer in algebraic form.

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Q23:

Given that where principal argument , and where principal argument , find .

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Q24:

Express in the form .

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D

Q25:

Given that and , determine .

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Lesson Worksheet: Operations on Complex Numbers in Polar Form Mathematics