Question

find multiplicative inverse of 3+2i​

Answer 1

$\huge{\fcolorbox{cyan}{pink}{Solution:-}}$

$\huge{\bf{\underline{Formula:-}}}$

${ \boxed { \pink{\frac{z}{ |z| } }}}$

where ,

z= conjugate of complex number

|z|= modulus of complex number

Conjugate:-

$\implies{ \pink{ \boxed{3 + 2i}}}$

Modulus:-

$\implies \sqrt{ {x}^{2} + y {}^{2} } \\ \\ \implies \sqrt{ {3}^{2} + {2}^{2} } \\ \\ \implies \sqrt{9 + 4} \\ \\ \implies{ \boxed{ \pink {\sqrt{13} }}}$

$\huge{\bf{\underline{Answer:-}}}$

putting the values in the formula:-

$\implies \frac{3 + 2i}{ \sqrt{13} } \\ \\ \implies { \boxed{ \pink{\frac{3}{ \sqrt{13} } + \frac{2i}{ \sqrt{13} } }}}$