## anonymous 4 years ago 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: .............?

1. anonymous

where i = $\sqrt{-1}$

2. anonymous

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

3. anonymous

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

4. anonymous

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

5. anonymous

Basically remember that: if z = a+bi |z| = sqrt[(a+bi)(a-bi)]

6. anonymous

okay noted, thanks again. love wolfram