Task A-2.4. (8 points)

Given are complex numbers $z=7-i, w=-3+4 i$. Determine $\left|\frac{z^{20}}{\bar{w}^{10}}\right|$.
Solution.

$\left|\frac{z^{20}}{\bar{w}^{10}}\right|=\frac{|z|^{20}}{|w|^{10}}=\frac{{\sqrt{7^{2}+1^{2}}}^{20}}{{\sqrt{3^{2}+4^{2}}}^{10}}=\frac{\sqrt{50}^{20}}{\sqrt{25}^{10}}=\frac{50^{10}}{5^{10}}=10^{10}$

For 4 points: good method with a minor error.

For 8 points: correct result and method.