Complex Numbers in Polar Form Calculator | Add, Subtract, Multiply, Divide

Add, Subtract, Multiply, and Divide Complex Numbers in Polar Form

Perform operations on complex numbers in polar form. Results shown in both rectangular and polar forms.

Complex Numbers in Polar Form

A complex number in polar form is written as \( Z = \rho \angle \theta \), where \( \rho > 0 \) is the magnitude and \( \theta \) is the argument (typically in the range \( [0°, 360°) \)).

Operations:

• Multiplication: \( \rho_1 \angle \theta_1 \times \rho_2 \angle \theta_2 = (\rho_1 \rho_2) \angle (\theta_1 + \theta_2) \)

• Division: \( \frac{\rho_1 \angle \theta_1}{\rho_2 \angle \theta_2} = \frac{\rho_1}{\rho_2} \angle (\theta_1 - \theta_2) \)

• Addition/Subtraction: Convert to rectangular form first.

\( Z_1 = \rho_1 \angle \theta_1 \)

\( \rho_1 \) (magnitude) *

\( \theta_1 \) (argument)

Unit

\( Z_2 = \rho_2 \angle \theta_2 \)

\( \rho_2 \) (magnitude) *

\( \theta_2 \) (argument)

Unit

Decimal places:

Enter magnitude > 0. Arguments can be in degrees or radians.

\( Z_1 \)

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\( Z_2 \)

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\( Z_1 + Z_2 \)

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\( Z_1 - Z_2 \)

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\( Z_1 \times Z_2 \)

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\( Z_1 \div Z_2 \)

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Enter values and click "Calculate All Operations"

Step-by-step solution will appear here after calculation.

Operations on Complex Numbers in Polar Form Calculator

Add, Subtract, Multiply, and Divide Complex Numbers in Polar Form

\( Z_1 = \rho_1 \angle \theta_1 \)

\( Z_2 = \rho_2 \angle \theta_2 \)

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