Question

find the multiplicative inverse of i/1+i​

Answer 1

Answer:

(4 - 2i) / 5

Step-by-step explanation:

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

$\frac{1}{z}$ = $\frac{2}{i + 2}$ = $\frac{2(i - 2)}{(i+2)(i-2)}$ = $\frac{2i - 4}{-1-4}$ = $\frac{2i - 4 }{-5}$ = $\frac{4 - 2i}{5}$