Question

the value |z|, if z satisfies the equation a(z+a^2)=2b-z, where a =-3.679+(-2.699)i and b = 0.474 + (-0.743)i, is: .............?

Answer 1

where
i = \[\sqrt{-1}\]

Answer 2

\[\large z = \frac{2b-a^{3}}{a+1} = \frac{-29.657 +88.446i}{-2.679-2.699i}\]
\[\large z = \frac{-159.265 -316.991i}{14.46}\]
\[\large z = -11.014 -21.92i\]
\[\large |z| = \sqrt{601.79} = 24.53\]

Answer 3

thanks! perfect, it's been a while since i've done imaginary numbers

Answer 4

yeah these numbers are kinda tedious to do by hand...i cheated with wolfram

Answer 5

Basically remember that:
if z = a+bi

|z| = sqrt[(a+bi)(a-bi)]

Answer 6

okay noted, thanks again.
love wolfram