Complex Numbers: De Moivres (1 Viewer)

[kevda1st]

Im having a problem with a question
Express in X+Yi form: (2 - i)^5
and (1 + 4i)^4

 

[tacogym27101990]

Im having a problem with a question
Express in X+Yi form: (2 - i)^5
and (1 + 4i)^4

convert them into mod-arg form
then use demoivres theorem on them. ie/ (rcis@)ⁿ = rⁿcisn@.
then convert back into the form x+iy.

 

[kevda1st]

yeh, i did that, but i dont get how you would covert the angle back to exact value form.

 

[Trebla]

Just evaluate the trig functions.

 

[gurmies]

evaluate the trigonometry inside the mod-arg form. You're not going to get pretty numbers though for x and y..

 

[tommykins]

If it's strictly De Moivres, do what the above has said.

Otherwise use binomial theorem.

 

[cutemouse]

Or Pascal's triangle

 

[tommykins]

Which more or less is binomial -_-"

 

[untouchablecuz]

Im having a problem with a question
Express in X+Yi form: (2 - i)^5
and (1 + 4i)^4

(2 - i)^5 = z^5 , where z = 2 - i

|z^5| = |z|^5

arg (z^5) = 5 arg z

From here use:

x = (|z|^5) cos x

y = (|z|^5) sin x