Question

In the abbreviation of the trigonometric form of a complex number, , what does thei represent? 

	A.	Imaginary unit
	B.	Index
	C.	Interval
	D.	Inverse

Find  and write the answer in standard form. 

	A.
	B.
	C.
	D.

Find  and write the answer in standard form. 

	A.
	B.
	C.
	D.

 

Answer 1

1)

The complex number

z = r cis θ

i represents Imaginary unit.

Option A is correct.

Answer 2

2)

Using De Moivre’s theorem:

If z =  r(cos θ + i sin θ) then zⁿ = [r(cos θ + i sin θ)]ⁿ =[rⁿ(cos nθ + i sin nθ)]

[2 (cos30° + i sin30°)]⁸ = (2)⁸(cos 8(30°) + i sin8(30°))

                                   =(2)⁸(cos 240° + i sin240°)

                                   =(2)⁸(cos (180°+60°) + i sin(180°+60°))

                                    =(2)⁸(- cos 60° - i sin 60°)

                                    =256(- (1/2) - i (√3/2))

                                    =-128 -128√3 i

Option D is correct.