Complex Number to Rectangular Form Calculator

Your details

Choose whether to start from polar form or rectangular form.
Unit for the phase angle. Degrees (0-360) or radians (0 to 2pi).
The modulus (distance from the origin) of the complex number. Must be >= 0.
The argument (angle from the positive real axis) in the chosen unit.
deg
Rectangular form (a + bi)
3.00001 + 3.99999i

The complex number written as a + bi.

Real part (a)3.000007
Imaginary part (b)3.999995
a (internal)3.00000715
b (internal)3.99999464
r (internal)5
Real part (a)3.00000715
Imaginary part (b)3.99999464
Modulus (r)5

Polar (5, 53.13) -> Rectangular 3.00001 + 3.99999i

  • The rectangular form is 3.00001 + 3.99999i, where 3.00001 is the real part and 3.99999 is the imaginary part.
  • The number lies in the first quadrant (positive real, positive imaginary) of the complex plane.
  • Modulus (distance from origin): 5. Argument: 53.13 degrees (0.927293 rad).

Next stepUse the rectangular form to add or subtract complex numbers easily. Multiply or divide complex numbers more easily in polar form by multiplying moduli and adding arguments.

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