Complex Number to Polar Form
This calculator converts a complex number from rectangular form $$(a + bi)$$ into polar form $$(r∠θ or r(cos θ + i sin θ))$$. It’s useful for students, engineers, and anyone working with complex numbers in electrical engineering or mathematics. Simply enter the real and imaginary parts, and the calculator returns the magnitude and angle in degrees and radians.
Complex Number to Polar Form Calculator
Polar Form Conversion Formula
- $$r$$ is the magnitude (modulus) of the complex number.
- $$\theta$$ is the angle (argument) in radians or degrees.
The polar form is written as $$z = r (\cos\theta + i \sin\theta)$$ or $$z = r \angle \theta$$
The polar form of a complex number is often used in trigonometry, signal processing, and electrical engineering because it simplifies multiplication and division of complex numbers. For example, multiplying two complex numbers in polar form involves multiplying their magnitudes and adding their angles. This form is especially helpful when visualizing complex numbers on the complex plane.
Entering $$a = 3$$ and $$b = 4$$, the calculator gives $$r = 5$$ and $$θ ≈ 53.13°$$.