Raise the number to the given power and write trigonometric

Raise the number to the given power and write trigonometric notation for the answer. [2(cos 60 degree + i sin 60 degree)]^3 (1 - i)^4 Raise the number to the given power and write standard notation for the answer (1 + i)^6 (1/2 + squareroot 3/2 i)^10 Find the squareroot s of -1+ i. Find the cube roots of 3 squareroot of 3 - 3i. Find and graph the fourth roots of 81. Find and graph the fifth roots of 1.

Solution

27. [2(cos 60 degree + i sin 60 degree )]³

According to De-moivre\'s theorem,

(cos theta + i sin theta)ⁿ= cos (n theta + i sin (n theta))

So we will get

2³(cos(3*60) degree + i sin(3*60 degree)) = 8(cos 180 degree + i sin 180 degree)