Question

Find multiplicative inverse of :

$\frac{3+4i}{4-5i}$

Answer 1

To find the multiplicative inverse, all you need to do is flip the function so the product of the number and its inverse$=1$

Then the inverse is:

$\frac{(4-5i)}{(3+4i)}$

Now let us simplify:

Multiply and divide by $(3-4i)$

$\Rightarrow \frac{(3-4i)(4-5i)}{(3+4i)(3-4i)}$

$\Rightarrow \frac{(12-15i-16i-20)}{\left(3^2\right)-(4i{)}^2}$

$\Rightarrow \frac{(-8-31i)}{(9+16)}=\frac{(-8-31i)}{25}$

$\Rightarrow -\frac{8}{25}-\frac{31}{25}i$.