Answer to Question #321471 in Complex Analysis for Simom

Question

Write Z = 4√(3) e^(7π/4)i in algebraic form

Answer 1

$z = 4\sqrt 3 {e^{\frac{{7\pi }}{4}i}} = 4\sqrt 3 (\cos \frac{{7\pi }}{4} + i\sin \frac{{7\pi }}{4}) = 4\sqrt 3 \left( {\frac{1}{{\sqrt 2 }} - \frac{1}{{\sqrt 2 }}i} \right) = 2\sqrt 2 \cdot \sqrt 3 - 2\sqrt 2 \cdot \sqrt 3 i = 2\sqrt 6 - 2\sqrt 6 i$

Answer: $2\sqrt 6 - 2\sqrt 6 i$