Complex Number to Polar Form Calculator
MathConvert a complex number from rectangular form (a + bi) to polar form (magnitude and phase).
Magnitude (r)
The distance from the origin to the point (a, b), sqrt(a^2+b^2).
Phase (degrees)
90.0000
The angle from the positive real axis, in the range (-180, 180].
Phase (radians)
1.570796
The phase angle in radians.
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Odeh Ahwal0people find this calculator helpful
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Frequently Asked Questions
What is polar form for a complex number?
Polar form expresses a complex number a+bi as r * exp(i*phi), using its distance from the origin (magnitude r) and angle from the positive real axis (phase phi) instead of separate real and imaginary parts.
How is the magnitude calculated?
The same way as distance in 2D coordinate geometry: magnitude = sqrt(a^2 + b^2), treating the real part as the x-coordinate and the imaginary part as the y-coordinate.
What is i in polar form?
i = 0 + 1i has magnitude 1 (it sits exactly 1 unit from the origin) and phase 90 degrees (pi/2 radians), since it lies straight up the imaginary axis.
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