Posted by jane on .
Express all the solutions to the following equations in a + bi form:
(a) z^2 +2z+4 = 0
(b) z^3 −8 = 0 [Hint: z^3 −8 = (z−2)(z^2 +2z+4)]
(c) 2z+iz = 3−i
thank you!

math 
MathMate,
I'll do the first one:
z²+2z+4=0
Use the quadratic formula:
z=(2±√(2²16))/2
=1±sqrt(3)
=1±(√3)i
The remaining questions are similar.
For #c,
2z+iz=3i
z(2+i)=3i
z=(3i)/(2+i)
the expression must be rationalized by multiplying both numerator and denominator by the conjugate of the denominator, namely (2i).
I'll leave the details to you.
Post your answer for checking if you wish. 
math 
jane,
thank you!
for part c I got 1i
but for part b, am I supposed to use the answer i got in part a to answer the question? 
math 
MathMate,
Yes, for #2, you can use the results of #1, since the expressions are identical.
For #3, 1i is correct!