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Question

The value of -1+i31-i30 is


A

215i

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B

215

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C

-215i

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D

65

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Solution

The correct option is C

-215i


Explanation for the correct answer:

The given expression -1+i31-i30 can be written as

-1+i31-i30=2-12+i321-i30

-1+i31-i30 =2ω1-i30 where, ω=-12+i32 is a cube root of unity ω3=1

-1+i31-i30=230ω301-i215

-1+i31-i30 =230ω3101-2i-115 (a-b2=a2-2ab+b2)

-1+i31-i30 =230110-215i15 [Multiply and divide by i]

-1+i31-i30 =-215×ii16 (i4n=1)

-1+i31-i30=-215i

Hence, the value of -1+i31-i30 is -215i.

Hence, Option (C) is the correct answer.


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