1/(1 - 2i) + 3/(1 + i) = ((1 + i) + 3(1 - 2i))/((1 - 2i)(1 + i))11−2i+31+i=(1+i)+3(1−2i)(1−2i)(1+i) (common denominator)
=(1 + i + 3 - 6i)/(1 + i - 2i + 2)=1+i+3−6i1+i−2i+2
=(4 - 5i)/(3 - i)=4−5i3−i
Now, we take that answer and multiply it by (3+4i)/(2-4i)3+4i2−4i.
((4-5i)/(3-i))((3+4i)/(2-4i)) = ((4-5i)(3+4i))/((3-i)(2-4i))(4−5i3−i)(3+4i2−4i)=(4−5i)(3+4i)(3−i)(2−4i)
=(12 + 16i - 15i - 20i^2)/(6 - 12i - 2i + 4i^2)=12+16i−15i−20i26−12i−2i+4i2
=(12 + 16i - 15i + 20)/(6 - 12i - 2i - 4)=12+16i−15i+206−12i−2i−4 (since i^2 = 1i2=1)
=(22 + i)/(2 - 14i)=22+i2−14i (by simplifying)
