a+bi Form Calculator: Polar to Rectangular Conversion

Your details

Choose the direction of conversion. Both modes compute the full set of related quantities.
Applies to the phase angle in both modes.
The modulus (distance from the origin) of the complex number. Must be >= 0.
The argument (angle from the positive real axis) of the complex number.
deg
Real part (a)First or second quadrant
3.535534

The real component of the rectangular form a + bi

Imaginary part (b)3.535534
Rectangular form3.535534 + 3.535534i
Modulus (|z|)5
Argument (deg)45deg
Argument (rad)0.785398rad
Conjugate (z*)3.535534 - 3.535534i
Exponential form5 * e^(0.785398i)
Polar form5 * cis(45°)
Real part (a)3.535534
Imaginary part (b)3.535534

z = 3.535534 + 3.535534i with modulus 5.

  • Rectangular form: 3.535534 + 3.535534i.
  • Modulus (distance from origin): 5.
  • Argument: 45 degrees (0.785398 radians).
  • Complex conjugate: 3.535534 - 3.535534i, which reflects the number across the real axis.

Next stepUse the conjugate to rationalise fractions with complex denominators, or use the modulus and argument in De Moivre's theorem for powers and roots.

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