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Q.
If $z_1=2\sqrt2(1+i)$ and $z_2=1+i\sqrt3$ , then $z_1^2\,\,z_2^3$ is equal to
Complex Numbers and Quadratic Equations
Solution:
We have $z_{1}=2\sqrt{2}\left(1+i\right)$
$z^{2}_{1}=8\left(1+i\right)^{2}\,8\left(1+i^{2}+2i\right)=16i$
Also, $z_{2}=1+i\sqrt{3}$
$\Rightarrow z^{3}_{2}=\left(1+i\sqrt{3}i\right)^{3}=1+3\sqrt{3}i^{3}+3\sqrt{3}i\left(1+i\sqrt{3}\right)$
$=1-3\sqrt{3}i+3\sqrt{3}i+9^{2}=-8$
So, $z^{2}_{1}z^{3}_{2}=16 \left(-8\right)i=-128i$