- #1

- 162

- 0

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

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

(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?