Icyo ari cyo cyose Imibare

,,, Matirise, - Cyangwa A ijambo i.

Precalculus · Complex-Numbers

Polar form of I

i

ku

  1. z = i = 0 + (1)i

    Read off the real and imaginary parts.

  2. |z| = \sqrt{0^2 + 1^2} = 1

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

  3. \theta = \arg z = \frac{\pi}{2} \approx 1.5708

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

  4. z = 1\left(\cos \frac{\pi}{2} + i\sin \frac{\pi}{2}\right) = 1 e^{i \frac{\pi}{2}}

    Polar and exponential forms (Euler).

i
1 e^{i \frac{\pi}{2}}