Question

Find The Multiplicative Inverse of 2 - 3i​

Answer 1

Answer:

Multiplicative inverse of 2 - 3i is 1/2-3i:

$\implies$ $\frac{1}{2 - 3i} \times \frac{2 + 3i}{2 + 3i}$

$\implies$ $\frac{2 + 3i}{(2)^{2} - {(3i)}^{2} }$

$\implies$ $\frac{2 + 3i}{13}$

$\implies$ $\frac{2}{13} + \frac{3}{13} i$

Answer 2

$\bold{ \large{Let \: , \: Z = 2 - 3i \:}}$

$\fbox{ \bold{\large{Conjugate \: Of \: Z : }}} \\ \\ \bold{\large{Conjugate \: Of \: Z \: = 2 + 3i}}$

$\fbox{\bold{\large{ \: Modulus \: Of \: Z \: : \: \sqrt{ {a}^{2} + {b}^{2} } }}} \\ \\ \bold{\large{Modulus \: Of \: Z \: = \sqrt{ {(2)}^{2} + {( - 3)}^{2} } = \sqrt{4 + 9} = \sqrt{13} }}$

$\fbox{\bold{ \huge{ \:Solution \: }}}$

$\fbox{ \bold{\large{multiplicative \: inverse \: of \: complex \: number = \frac{conjugate \: of \: complex \: number}{square \: of \: modulus \: of \: complex \: number} }}} \\ \\ \bold{\large{multiplicative \: inverse \: of \: z \: = ( \frac{2 + 3i}{ { ( \: \sqrt{13} \: ) }^{2} } ) }} \\ \\ \bold{\large{multiplicative \: inverse \: of \: z \: = \frac{2 + 3i}{13} }} \\ \\ \bold{ \large{multiplicative \: inverse \: of \: z \: = \frac{2}{13} + \frac{3i}{13} }}$