Question

How do you simplify `(5-3i)/(1+2i)`?

Answer 1

`(5-3i)/(1+2i) = -(1+13i)/5`

Explanation:

To simplify a fraction with a complex number in the denominator, we simply multiply the numerator and the denominator by the complex conjugate of the denominator.

`(5-3i)/(1+2i)= (5-3i)/(1+2i)*(1-2i)/(1-2i)`

Note that this will leave us with a real number for the denominator.

`(5-3i)/(1+2i)*(1-2i)/(1-2i)=(5 -10i -3i -6)/(1 -2i +2i +4) = -(1+13i)/5`