Question

Write the complex number in the form a + bi. 8(cos 30° + i sin 30°)

Answer 1

`4√(3)+4i`

Explanation:

`8(\cos 30^\circ + i \sin 30^\circ) = 8 (√(3))/(2)+i8(1)/(2)=4√(3)+4i`

Answer 2

`4√(3) +4i`

Explanation:

Use the Euler's Formula, which is given by:

`r e^(i \theta) = r(cos(\theta)+i sin(\theta))`

Where:

`a=rcos(\theta)\\b=rsin(\theta)\\\\tan(\theta)=(b)/(a)`

From the problem, you can see:

`r=8\\\theta=30^(\circ)`

So:

`a=8*cos(30)=4 √(3) \approx6.928\\b=8*sin(30)=4`

Therefore, the complex number in its rectangular form is:

`4√(3) +4i`