# Math Help - complex numbers

1. ## complex numbers

I am having trouble with these 2 questions

Find the complex number z such that (5+2i)+ ((−3−2i)/z)=5i

and

Find the complex number z such that (2−2i)z+(1−4i)z bar=4+5i

any help would be great
thanks

2. Originally Posted by kblythe
I am having trouble with these 2 questions

Find the complex number z such that (5+2i)+ ((−3−2i)/z)=5i

and

Find the complex number z such that (2−2i)z+(1−4i)z bar=4+5i

any help would be great
thanks
1) $\frac{-3 - 2i}{z} = 3i - 5 \Rightarrow \frac{z}{-3 - 2i} = \frac{1}{-5 + 3i} \Rightarrow z = \frac{-3 - 2i}{-5 + 3i}$. Your job is to express this answer in cartesian form.

2) Let $z = x + iy$:

$(2 - 2i)(x + iy) + (1 - 4i)(x - iy) = 4 + 5i$.

Expand and equate the real and imaginary parts on each side. This will give you two simultaneous equations that you must solve for x and y.

If you need more help, please show all your work and say where you're stuck.