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))
