Question

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

Answer 1

Answer:

$4\sqrt{3} +4i$

Step-by-step explanation:

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

$r e^{i \theta} = r(cos(\theta)+i sin(\theta))$

Where:

$a=rcos(\theta)\\b=rsin(\theta)\\\\tan(\theta)=\frac{b}{a}$

From the problem, you can see:

$r=8\\\theta=30^{\circ}$

So:

$a=8*cos(30)=4 \sqrt{3} \approx6.928\\b=8*sin(30)=4$

Therefore, the complex number in its rectangular form is:

$4\sqrt{3} +4i$

Answer 2

Answer:

$4\sqrt{3}+4i$

Step-by-step explanation:

$8(\cos 30^\circ + i \sin 30^\circ) = 8 \frac{\sqrt{3}}{2}+i8\frac{1}{2}=4\sqrt{3}+4i$