Question

find multiplicative inverse-1-√3 i ​

Answer 1

$\underline{\underline{\orange{\textbf{Step - By - Step - Explanation : -}}}}$

To Find :

• multiplicative Inverse of 1 - √3i

Solution :

Multiplcative inverse of 1 - √3i is 1/1 - √3i

Rationalising the denominator :

$\sf \: = \frac{1}{1 - \sqrt{3}i } \times \frac{1 + \sqrt{3}i }{1 + \sqrt{3}i } \\ \\ = \sf \: \frac{1 + \sqrt{3}i }{(1 - \sqrt{3}i)(1 + \sqrt{3} i)} \\ \\ \sf \: = \frac{1 + \sqrt{3i} }{(1 {)}^{2} - (\sqrt{3}i) {}^{2} } \\ \\ \sf \: = \frac{1 + \sqrt{3}i }{1 - 3 {i}^{2} } \\ \\ \sf \: we \: know \: that \bf \: {i}^{2} = - 1 \\ \\ \sf \: = \frac{1 + \sqrt{3}i }{1 + 3} \\ \\ \sf \: = \frac{1 + \sqrt{3} i}{4}$