Find the following product and give the result in the form a

Find the following product, and give the result in the form a+bi using exact values.

2(cos30°+isin30°)•3(cos90°+isin90°)=

Solution

theta=90 degree=pi/2 radian

We can convert a complex number to exponential form in the following manner

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

therefore 2(cos 30 + isin 30)= 2 e^ipi/6

3(cos 90 + isin90)= 3 e^ipi/2

2e^ipi/6*3 e^ipi/2=6 e^{i 2pi/3}

6(cos 2pi/3 + i sin 2pi/3)