Question

Multiplicative inverse of -1+ root3i

Answer 1

Answer:

$\large{\bold{-\frac{(1+\sqrt{3}i)}{4}}}$

Step-by-step explanation:

Multiplicative of a number is a number, whose product with the original number gives product as 1.

Given No.

$-1+\sqrt{3}i$

Its Multiplicative inverse is

$\frac{1}{-1+\sqrt{3}i}\\\\rationalizing\;denominator\\\\=\frac{1}{(-1+\sqrt{3}i)}\times\frac{{-1-\sqrt{3}i}}{(-1-\sqrt{3}i)}\\\\=\frac{-1-\sqrt{3}i}{1^2+(\sqrt{3})^2}\\\\=-\frac{(1+\sqrt{3}i)}{4}$

HOPE IT HELPS