# If Z = ( 1 + I 1 − I ) Then Z4 Equals - Mathematics

MCQ

If $z = \left( \frac{1 + i}{1 - i} \right)$ then z4 equals

#### Options

•  1

• −1

• 0

• none of these

#### Solution

1

$\text {Let } z = \frac{1 + i}{1 - i}$

Rationalising the denominator:

$z=\frac{1 + i}{1 - i}\times\frac{1 + i}{1 + i}$

$\Rightarrow z = \frac{1 + i^2 + 2i}{1 - i^2}$

$\Rightarrow z = \frac{2i}{2}$

$\Rightarrow z = i$

$\Rightarrow z^4 = i^4$

$\text { Since} i^2 = - 1,\text { we have }:$

$\Rightarrow z^4 = i^2 \times i^2$

$\Rightarrow z^4 = 1$

Is there an error in this question or solution?

#### APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 13 Complex Numbers
Q 19 | Page 65