Question

solve....



i'll draw the equation

Answer 1

\[(3\sqrt{2} (\cos 45 + i \sin 45 )^{3}\]

Answer 2

keep in a+bi form

Answer 3

\[(\frac{\sqrt{3}}{2}(\cos(45)+i \cdot \sin(45))^3\]
\[r e^{i \cdot \theta}= r (\cos(\theta)+i \cdot \sin(\theta) )\]
\[(r e^ {i \theta})^3=(r \cos(\theta) + i \sin(\theta) )^3\]
\[(\frac{\sqrt{3}}{2} e ^{i \frac{\sqrt{2}}{2}})^3= ( \frac{\sqrt{3}}{2} \cos(\frac{\sqrt{2}}{2})+i \cdot \sin(\frac{\sqrt{2}}{2}))^2\]
So what do you get when you in the following form:
\[r' e^{ i \theta'}\]
\[(\frac{\sqrt{3}}{2} e^{i \cdot \frac{\sqrt{2}}{2}})^3\]
\[\text{What is } r' \text{ and what is } \theta' ? \]