Perform the operation shown below and leave the result in trigonometric form.

Question

Quizplus · Accepted Answer

The given operation involves multiplying by $e^{\frac{\pi i}{6}}$, which corresponds to a rotation of $\frac{\pi}{6}$ radians counterclockwise in the complex plane. This rotation transforms $1+i$ to $\sqrt{2}e^{\frac{\pi i}{4}}$. Multiplying $1+i$ by $\sqrt{2}e^{\frac{\pi i}{4}}$ gives $(1+i)\cdot\sqrt{2}e^{\frac{\pi i}{4}}=\boxed{\sqrt{2}+i\sqrt{2}}$ which is in trigonometric form.

Perform the Operation Shown Below and Leave the Result in Trigonometric