Complex Number to Polar Form Calculator
Convert nonzero a + bi to modulus r and principal argument θ in degrees and radians.
Formula
r = √(a²+b²); θ = arg(a+bi); z = r(cos θ+i sin θ).
Modulus r ≈ (5) · Argument in radians ≈ (0.927295218) · Argument in degrees ≈ (0.927295218)×180÷pi
How to use
- Enter the real part a.
- Enter the imaginary coefficient b; do not enter zero for both.
- Read r and θ for polar or trigonometric form.
Examples
- 3+4i has r=5 and θ≈53.130102°.
Frequently asked questions
Which angle range is used?
−180° < θ ≤ 180°, equivalent to −π < θ ≤ π.
Can I convert zero?
Zero has modulus 0 but no unique argument, so this tool requires a nonzero number.
Is trigonometric form different?
It uses the same r and θ: z=r(cos θ+i sin θ), also written r cis θ.
Sources
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