Question

Simplify the following expressions by using trigonometric form and De Moivre's theorem

a. (√3-i)^4

b. (-4+4i√3)^5

c.(2+3i)^4

d. (4-i)^6

Answer 1

Tell you what -- why don't you simplify them and we'll check your answers.

To get started on (a)
√3-i = 2cis -π/6
so, (√3-i)^4 = 16cis -2π/3
now just convert that back to rectangular values.

Answer 2

but i don't get the first one

Answer 3

You need to review the methods of expressing complex numbers as a+bi and r cisθ. Surely your text has a discussion of the topic.

Also, a simple google on "complex numbers polar" will turn up may explanations and examples.

√3-i can be plotted as the point (√3,-1) in the x-y plane.

Now, measuring from the x-axis, that point is at an angle of -π/6, and is 2 units from the origin. Hence the polar form.

Answer 4

What do I do next after that?