Question

How do you write `((5-2i)+(5+3i))/((1+i)-(2-4i))` in standard form?

Answer 1

`-5/26 -51/26 i`

Explanation:

Add like terms in the numerator and denominator:
`((5+5) + (-2i +3i))/((1+ -2)+(i--4i)) = (10+i)/(-1+5i)`

Multiple by `1` using the conjugate of the denominator:
:`(10+i)/(-1+5i) * (-1-5i)/(-1-5i) = (-10-50i-i-5i^2)/(1-25i^2)`

Remember that `i^2 = -1`:

`(-10-50i-i+5)/(1+25) = (-5-51i)/(26)`

Put in standard form: `-5/26 -51/26 i`