Complex Number to Trigonometric Form Calculator

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The real component of z = a + bi.
The coefficient of i in z = a + bi.
Choose whether the argument (angle) is displayed in degrees or radians.
Number of decimal places shown in the result.
Modulus |z|Outside unit circle
1.4142

Distance from the origin to z in the complex plane.

Argument phi (degrees)45deg
Argument phi (radians)0.785398rad
Trigonometric form1.4142(cos(pi/4) + i*sin(pi/4))
Exponential (Euler) form1.4142 * e^(i * pi/4)
r cos(phi)1
r sin(phi)1
r cos(phi) = a (real)1
r sin(phi) = b (imaginary)1

z = 1 + 1i has modulus 1.4142 and argument 45.0000 deg.

  • The modulus |z| = 1.4142 is the distance from the origin to z in the Argand plane.
  • The argument phi = 45.0000 deg places z in the Quadrant I (a > 0, b > 0).

Next stepTo multiply two complex numbers in polar form, multiply their moduli and add their arguments: |z1*z2| = |z1|*|z2|, phi(z1*z2) = phi1 + phi2.

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