Question

What us multiplicative inverse of 1+I/1-i

Answer 1

anss. s. s. s. s. s s.

Answer 2

The answer is '1/i'.

GIVEN

Algebraic expression- (1+i) /(1-i)

TO FIND

The multiplicative inverse.

SOLUTION

The above problem can be simply solved as follows;

Let 'z' be the complicated number

where,

z = a + ib

Multiplicative inverse;

1/z = z̅/|z|²

|z| = √(a)² + (b)²

In the given question,

z = 1+i/1-i

Rationalising

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

$= \frac{(1 +i)^{2} }{ {1}^{2} - {i}^{2} }$

$= \frac{1 + {i}^{2} + 2i }{1 + 1}$

$= \frac{1 - 1 + 2i}{1 + 1} = \frac{2i}{2}$

= i

Multiplicative inverse of 'i' = 1/i

Hence, The answer is '1/i'.

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