Question

How do you divide `(1+7i) / (9-5i)` in trigonometric form?

Answer 1

The result of division is `1/53( -13+34i)`
Its trignometrical form `(sqrt1325)/53 (-13/sqrt1325 +34/sqrt1325 i)`

Explanation:

First of all multiply the numerator and the denominator by the conjugate of denominator.

`((1+7i)(9+5i))/((9-5i)(9+5i))= (-26+68i)/106`

=`1/53( -13+34i)`

Now Modulus would be `sqrt (13^2 +34^2)=sqrt1325`

The number can now be written as `(sqrt1325)/53 (-13/sqrt1325 +34/sqrt1325 i)`

The number now is in trignometrical form its Modulus is `sqrt1325 /53` and arg is `tan^-1 (34/(-13))`