I need to solve the following equation, i would appreciate some help. z^2 − (3 − 2i)z + 1− 3i?
Update:
There is a second problem
z^2 - 2z + i = 0
I get solutions
1 - sqrt(1 - i),
1 + sqrt(1 - i)
but i'm told these are not correct, could anybody help me out?
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Verified answer
Use the quadratic formula.
z = [- (-3 + 2i) (+,-) sqrt((-3+ 2i)^2 - 4(1 - 3i))]/2
= [(3 - 2i) (+,-) 1]/2
= 2 - i or 1 - i.
I hope that helps!