Quick question about complex numbers !!!!

so i know how to add, subtract, and mulitply, but im having trouble simplying this type of equation with the inverse.
For example how do i go from this [(1/20)+(1/j10)]^-1 ...to being equal to this 4+j8

Another example is [(1/-j1250)+(1/j500)]^-1 to being equal to 1500-j500

Any ideas ?? Any help will be appreciated, thanks !

You must know that a^(-1) = 1/a

[(1/20)+(1/j10)]^(-1) =

((10j + 20)/200j)^(-1) =

((2 + j)/20j)^(-1) =

((-20j)(2 + j)/400))^(-1) =

((-40j - 20j²)/400))^(-1) =

((2 - 4j)/40))^(-1) =

40/(2 - 4j) =

40(2 + 4j)/20 =

2(2 + 4j) =

4 + 8j