Convert Complex Number to Polar Form (z) - Definition, Formula and Example

Definition:

In polar representation, a complex number is denoted in terms of two variables namely r and ϑ, where r is the modulus of complex number and ϑ is the angle with the positive direction of x-axis. Polar coordinates expresses the location of a point as (r, ϑ).

Formula:

z = r ( cos ϑ + i sin ϑ ) r = √ x2 + y2 ϑ = tan-1 (y / x)
Where,
x, y - triangle sides r - Modulus of complex number z - Polar representation ϑ - Angle
Example:

Find the polar form and represent graphically the complex number 7 - 5j.

Given

x = 7 y = 5

To Convert

Complex Number to Polar Form (z)

Solution:
Step 1:
r = √x2 + y2
r = √ 52 + 72

r = 8.602

Step 2:
ϑ = tan-1 (y / x)

ϑ = tan-1 (5 / 7) ϑ = 36°

Step 3:
Polar representation (z) = r ( cos ϑ + i sin ϑ )

(z) = 8.602 ( cos 36° + i sin 36°) Hence the polar representation value of complex number is calculated.

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