What is the multiplicative inverse of

5√2- 4i

Please show solution. Thank you in advance.
Sincerely appreciates your help.

I'll give two ways. Let z = a+ bi be the inverse. Then
1) (5√2- 4i )(a + bi) = 1. After multiplying you get simple equations for a and b.

2) the inverse is 1/(5√2- 4i). To see the natural form of this multiply top and bottom by
5√2+4i and simplify.

Do the problem both ways to check your answer and to see which is easiest.

the multiplicative inverse of 5√2- 4i is 1/(5√2- 4i)