Question

How do you simplify `(4+2i)/(1-i)`?

Answer 1

`(4+2i)/(1-i) = 1+3i`

Explanation:

Given
`color(white)("XXX")(4+2i)/(1-i)`

Multiply numerator and denominator by the complex conjugate of the denominator
`color(white)("XXX")(4+2i)/(1-i) xx (1+i)/(1+i)`

`color(white)("XXX")=(4+2i+4i+2i^2)/(1-i^2`

`color(white)("XXX")=(4+6i-2)/(1-(-1))`

`color(white)("XXX")=(2+6i)/2`

`color(white)("XXX")=1+3i`