Question

Find the multiplicative inverse of √5+3i.

Answer 1

$multiplivtive \: inverse \: of \sqrt{5} + 3i = \frac{1}{ \sqrt{5} + 3i}$
$\frac{1}{ \sqrt{5 } + 3i } \times \frac{ \sqrt{5} - 3i }{ \sqrt{5} -3i}$
$= \frac{ \sqrt{5} - 3i }{5 + 9}$
$= \frac{ \sqrt{5} - 3i}{14}$

It is the Multiplicative inverse of Root 5 - 3i
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Answer 2

Answer:

The multiplicative inverse of the function is $\frac{\sqrt5}{14}-\frac{3i}{14}$

Step-by-step explanation:        

Given : Expression $\sqrt5+3i$

To find : The multiplicative inverse of expression ?

Solution :

Multiplicative inverse of $z=z^{-1}=\frac{1}{z}$

Let  $z=\sqrt5+3i$

Multiplicative inverse of $z=\sqrt5+3i$ is given by $\frac{1}{z}=\frac{1}{\sqrt5+3i}$

Rationalize the expression,

$\frac{1}{z}=\frac{1}{\sqrt5+3i}\times \frac{\sqrt5+3i}{\sqrt5+3i}$

$\frac{1}{z}=\frac{\sqrt5-3i}{(\sqrt5-3i)(\sqrt5+3i)}$

$\frac{1}{z}=\frac{\sqrt5-3i}{(\sqrt5)^2-(3i)^2}$

$\frac{1}{z}=\frac{\sqrt5-3i}{5+9}$

$\frac{1}{z}=\frac{\sqrt5-3i}{14}$

$\frac{1}{z}=\frac{\sqrt5}{14}-\frac{3i}{14}$

Therefore, The multiplicative inverse of the function is $\frac{\sqrt5}{14}-\frac{3i}{14}$