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Question

If iz4+1=0, then z can take the value:


A

1+i2

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B

cosπ8+isinπ8

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C

14i

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D

i

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Solution

The correct option is B

cosπ8+isinπ8


Explanation for the correct option:

Find the value of z:

iz4+1=0iz4=-1z4=-1i

Multiplying numerator and denominator by i, we get

z4=-ii2z4=iz41/4=i1/4z=0+i1/4=isinπ2+cosπ21/4=isinπ8+cosπ8

Hence, option B is correct.


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