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 |
| 8.0622577482985 |
cos(θ) = 0.49613893835683
Calculate sin(θ):
b = rsin(θ):
| sin(θ) = | b |
| r |
| sin(θ) = | -7 |
| 8.0622577482985 |
sin(θ) = -0.86824314212446
Calculate tan(θ):
| tan(θ) = | sin(θ) |
| cos(θ) |
| tan(θ) = | -0.86824314212446 |
| 0.49613893835683 |
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))
What is the Answer?
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.
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?)
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
