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Precalculus · Complex-Numbers

Polar form of sqrt(3) + I

\sqrt{3} + i

Step by step

  1. z = \sqrt{3} + i = \sqrt{3} + (1)i

    Read off the real and imaginary parts.

  2. |z| = \sqrt{\sqrt{3}^2 + 1^2} = 2

    The modulus is the distance from the origin (Pythagoras).

  3. \theta = \arg z = \frac{\pi}{6} \approx 0.52360

    The argument is the angle from the positive real axis (watch the quadrant).

  4. z = 2\left(\cos \frac{\pi}{6} + i\sin \frac{\pi}{6}\right) = 2 e^{i \frac{\pi}{6}}

    Polar and exponential forms (Euler).

Reveal the answer
2 e^{i \frac{\pi}{6}}