Question

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

Answer 1

`(2+5i)/(1-i)= -3/2 + 7/2i`

Explanation:

The conjugate of a complex number `a+bi` is `a-bi`. The product of a complex number and its conjugate is a real number. We will use this fact to produce a real number in the denominator by multiplying the numerator and denominator by the conjugate of the denominator.

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

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

`= (-3+7i)/2`

`= -3/2 + 7/2i`