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Evaluate : [i^(18)+(1/i)^(25)]^3...

Evaluate : `[i^(18)+(1/i)^(25)]^3`

A

`2i`

B

`3-2i`

C

`2-2i`

D

`2`

Text Solution

Verified by Experts

The correct Answer is:
C
`[ i^(18)+((1)/(i))^(25)] ^(3)=[i^(( 4xx4)+2)+(1)/(i^(25))]^(3)`
`=[i^(4xx4)*i^(2)+(1)/(i^(4xx6)*i)]^(3)=[1*i^(2)+(1)/(1*i)]^(3)`
`=[i^(2)+(i)/(i^(2))]^(3)=[-1-i]^(3)=[-(1+i)]^(3) `
`=[i^(2)+(i)/(i^(2))]^(3)=[-1-i^(3)] =[-(1+i)]^(3)`
`=-(1+i)^(3)=- [1^(3)+i^(3) + 3*1*i(1+ i)] `
`=-[1-i+3i+3i^(2)] =-[1+2i-3]`
` = - [-2+2i]=2-2i`
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