Using Demoivres Theorem

Convert 4-7i into polar form

##### Polar Form Definition:

z = r(cos(θ) + isin(θ)) where:
a = rcos(θ) and b = rsin(θ)
r = √a2 +b2

In this case, a = 4 and b = -7

##### Calculate r:

r = √a2 + b2

r = √42 + -72

r = √16 + 49

r = √65

r = 8.0622577482985

##### Calculate cos(θ):

a = rcos(θ):

 cos(θ)  = a r

 cos(θ)  = 4 8.06226

cos(θ) = 0.49613893835683

##### Calculate sin(θ):

b = rsin(θ):

 sin(θ)  = b r

 sin(θ)  = -7 8.06226

sin(θ) = -0.86824314212446

##### Calculate tan(θ):

 tan(θ)  = sin(θ) cos(θ)

 tan(θ)  = -0.868243 0.496139

tan(θ) = -1.75

θ = arctan(-1.75)

θ = -1.0516502125484

##### Calculate z:

z = r(cos(θ) + isin(θ))

z = 8.0622577482985(cos(-1.0516502125484) + isin(-1.0516502125484))

#### You have 2 free calculationss remaining

z = 8.0622577482985(cos(-1.0516502125484) + isin(-1.0516502125484))
##### How does the Demoivres Theorem Calculator work?
Free Demoivres Theorem Calculator - Using Demoivres Theorem, this calculator performs the following:
1) Evaluates (acis(θ))n
2) Converts a + bi into Polar form
3) Converts Polar form to Rectangular (Standard) Form
This calculator has 6 inputs.

### What 1 formula is used for the Demoivres Theorem Calculator?

if z = rcis(θ), then zn = rncis(n?)

For more math formulas, check out our Formula Dossier

### What 3 concepts are covered in the Demoivres Theorem Calculator?

demoivres theorem
A formula useful for finding powers and roots of complex numbers
z = rcis(θ), then zn = rncis(nθ)
imaginary number
a real number multiplied by the imaginary unit i, which is defined by its property i2 = -1.
polar
a two-dimensional coordinate system in which each point on a plane is determined by a distance from a reference point and an angle from a reference direction