# Worksheet: Exponential Form of a Complex Number

In this worksheet, we will practice converting a complex number from the algebraic to the exponential form (Euler’s form) and vice versa.

Q1:

Put in exponential form.

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• E

Q2:

Express the complex number in the form of .

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Q3:

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

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Q4:

Put the number in exponential form.

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Q5:

Given that , write in exponential form.

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Q6:

Given that , find in exponential form.

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Q7:

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

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Q8:

Given that and , express in the form .

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Q9:

Put in exponential form.

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Q10:

Given that , where and , find and .

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• C,
• D,

Q11:

Put in algebraic form.

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Q12:

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

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Q13:

Put in exponential form.

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• E

Q14:

Given that , find the algebraic form of .

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Q15:

Express in exponential form.

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Q16:

Find the numerical value of .

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Q17:

Express in exponential form.

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Q18:

Express in exponential form.

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Q19:

Given that , express in exponential form.

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Q20:

Given that , , and , find all the possible values of , expressing them in exponential form.

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• D, , and

Q21:

Put in exponential form.

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• E

Q22:

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Q23:

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Q24:

Put in exponential form.

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• D

Q25:

Given that , determine the value of , giving your answer in exponential form.

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