# Linear algebra - find all solutions with complex numbers

(a)Find all t $$\epsilon C$$ such that $$t^{2}$$ + 3t + (3-i) = 0. Express your solution(s) in teh form x+iy where x,y $$\epsilon R.$$

(b) Prove that | 1+iz | = | 1-iz | if and only if z is real.

Okay so I tried to use the quadratic formula to find the roots to find the solutions, but I am stuck because I have a complex number within the square roots.

t = -b +/- sqrt(b^2 - 4ac) / 2a
t = -3 +/- sqrt[(-3)^2 - 4(1)(3-i)] / 2(1)
t = -3 +/- sqrt(-3 + 4i) / 2

what do i do?

also for question (b), where do I even start?

matt grime