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Question

Evaluate i18+(1i)253

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Solution

Given data : z=[i18+(1i)25]3

Using exponent property

z=[(i)4×4+2+1(i)4×6+1]3

=[(i)2+1i]3 [ i4=1]

Arrange in numerator form

z=[(i)2+1i×ii]3

=[(i)2+ii2]3 i2=1

=[1i]3

z=[i18+(1i)25]3 =[1i]3

=(1+i)3

Apply (A+B)3 formula

z=[(1)3+(i)3+3(1)2+3(1)(i)2]

=[1+i3+3i+3i+3i2]

=[1i+3i3]

=[2+2i]

=22i

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