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Question

Express (1+i)2n+1(1i)2n1,nN in the modulus-amplitude form

A
{2(cos0o+isin0o)if n is even2(cosπisinπ)if n is odd
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B
{2(cos0oisin0o)if n is even2(cosπ+isinπ)if n is odd
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C
{2(cos0o+isin0o)if n is even2(cosπ+isinπ)if n is odd
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D
{2(cos0oisin0o)if n is even2(cosπisinπ)if n is odd
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Solution

The correct option is C {2(cos0o+isin0o)if n is even2(cosπ+isinπ)if n is odd
The equation can be simplified to:
(1+i1i)2n.(1+i).(1i)=((1+i)(1+i)(1i)(1+i))2n.2=(2i2)2n.2=2.i2n=2.(1)nneven:2=2(cos0o+isin0o)nodd:2=2(cosπ+isinπ)
Hence, (c) is correct.

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