Question

Calculate 6+9i/-1+4i

Answer 1

Multiply the numerator and denominator by the conjugate of the denominator:

`(6+9i)/(-1+4i) * (-1-4i)/(-1-4i) = ((6+9i)(-1-4i))/((-1)^2-(4i)^2)`

Simplify:

`((6+9i)(-1-4i))/((-1)^2-(4i)^2) = (-6-9i-24i-36i^2)/(1-16i^2) = (-6-33i-36i^2)/(1-16i^2) = (-6-33i+36)/(1+16) = \boxed{(30-33i)/(17)}`