Question

I need help with number 2 and can you please do it the same way as the paper so I can understand it better.

Answer 1

The cosine and sine values are reversed.

`4\cdot cis\mleft((\pi)/(3)\mright)=2+2\sqrt[]{3i}`

Explanation:

We can rewrite the function as follows:

`a\cdot cis(\theta)=a\cdot\cos (\theta)+ai\cdot\sin \theta`

In this case, then it would be:

`\begin{gathered} 4\cdot cis\mleft((\pi)/(3)\mright)=4\cdot\cos \mleft((\pi)/(3)\mright)+4i\cdot\sin \mleft((\pi)/(3)\mright) \\ \cos \mleft((\pi)/(3)\mright)=(1)/(2) \\ \sin \mleft((\pi)/(3)\mright)=\frac{\sqrt[]{3}}{2} \\ \text{ replacing} \\ 4\cdot cis\mleft((\pi)/(3)\mright)=4\cdot(1)/(2)+4i\cdot\frac{\sqrt[]{3}}{2} \\ 4\cdot cis\mleft((\pi)/(3)\mright)=2+2\sqrt[]{3i} \end{gathered}`

What it means is that the error was that it was wrong when calculating the cosine and the sine, it has the values inverted