Question

If z=(1+I/1-I)
then z4 equals.

Answer 1

Given :  Z  = (1 + i)/(1 - i)

To Find : Z⁴

Solution:

Z  = (1 + i)/(1 - i)

on rationalizing

Z = (1 + i)(1 + i) /(1 - i)(1 + i)

=>  Z = ( 1 + i²  + 2i)/( 1 - i²)

i² = - 1

=>    Z = ( 1 -1  + 2i)/( 1 - (-1))

=> Z = 2i/2

=> Z = i  

Z⁴ = i⁴

=> Z⁴ = (i²)²

=> Z⁴ = ( - 1)²

=> Z⁴ = 1

Z⁴ = 1   if  Z  = (1 + i)/(1 - i)

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Answer 2

Given : Z = (1 + i)/(1 - i)

To Find : Z⁴

Solution:

Z = (1 + i)/(1 - i)

on rationalizing

Z = (1 + i)(1 + i) /(1 - i)(1 + i)

=> Z = ( 1 + i² + 2i)/( 1 - i²)

i² = - 1

=> Z = ( 1 -1 + 2i)/( 1 - (-1))

=> Z = 2i/2

=> Z = i

Z⁴ = i⁴

=> Z⁴ = (i²)²

=> Z⁴ = ( - 1)²

=> Z⁴ = 1

Z⁴ = 1 if Z = (1 + i)/(1 - i)