Question

using de-moivre formula
solve (2+4i)^2

help , i really have no idea

Answer 1

As far as I am concerned, de-moivre is applied to complex numbers in polar coordinate form, so you might want to get the above number first into it's complex form.

Answer 2

the above number into it's complex polar coordinate form*

Answer 3

first convert it into polar or trigonometrical form without squaring
then apply this \[\LARGE{(\cos \theta + i \sin \theta)^n=\cos n \theta + i \sin n \theta.}\]

Answer 4

sorry @greysica
\[\LARGE{(|z|\cos \theta + i |z|\sin \theta)^n=|z|(\cos n \theta + i \sin n \theta).}\]

Answer 5

okay , what should I do ?

Answer 6

Again sorry!! @greysica
\[\LARGE{(|z|\cos \theta + i |z|\sin \theta)^n=|z|^n(\cos n \theta + i \sin n \theta).}\]

Answer 7

http://en.wikipedia.org/wiki/De_Moivre%27s_formula

Answer 8

i know i know that's the formula , I mean how I do the calculation with that formula ?

Answer 9

oh !!!!!!!
well u must forget square first then put the value of |z|; \[|z|=\sqrt{x^2+y^2}.\]& theta \[\theta = \tan^{-1}\frac{y}{x}\]in ur polar form if ur z = x+iy.
ok!
u will get then\[|z|(\cos \theta + i \sin \theta)\]
now square it
k!
& apply de moivre:)
as u know the formula.

Answer 10

i dont get it :(
can u do calculation for me ?

Answer 11

Do the formulas above make sense to you @greysica, because they should before you apply them.

De-Moivre's law works for polar coordinates, and to get an equation into polar coordinate it has to remain an unique identity, you require two things for that:

1. The distance from the origin which is given by Pythagoras' theorem.
2. The angle between x-axis and the line which is given by the inverse tan function (trigonometry)

Answer 12

So you are just solving for values to plug into the equation, the formula itself will then translate your values again into rectangular coordinates. You can double check in the end, because it's just a binomial.

Answer 13

can u give me an example ?

Answer 14

anyone help ? @phi ?

Answer 15

change to polar coordinates using pythagoras to find the magnitude and tangent to find the angle