Question

multiplicative inverse of 3-5i​

Answer 1

Step-by-step explanation:

Multiplicative inverse means reciprocal....

Answer 2

Given,

The number given$\[ = 3 - 5i\]$

Solution,

Formula used, the multipicative inverse of a is given as$\[\frac{1}{a}\].$  

Convert the given number into standard form.

Therefore,

$\[\begin{array}{l} \Rightarrow \frac{1}{{3 - 5i}} \times \frac{{3 + 5i}}{{3 + 5i}}\\ \Rightarrow \frac{{3 + 5i}}{{{{\left( 3 \right)}^2} - {{\left( {5i} \right)}^2}}}\\ \Rightarrow \frac{{3 + 5i}}{{9 + 25}}\\ \Rightarrow \frac{{3 + 5i}}{{34}}\end{array}\]$

Hence, the multiplicative inverse is $\[\frac{{3 + 5i}}{{34}}.\]$