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

1 Answer
Feb 18, 2017

-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