# Solving unknown complex number w

I have a complex number $$w$$= a + bi such that $$w\bar{w}$$ = 25 and $$w$$ + $$\bar{w}$$ = 8. I assume from this that the complex number in question hast two values. I've already solved the $$w$$ + $$\bar{w}$$ = 8 equation, but I'm having problems with $$w\bar{w}$$ = 25.

I've narrowed the equation down to $$a^2$$+$$b^2$$=25 but I don't know how to solve the rest. Or if I'm at least on right tracks.

I suck at this stuff and I've tried over and over again but just can't make it.

$$w+\bar w=8$$ means $$a=4$$. Then we can find $$b$$ using $$a^2+b^2=25$$.