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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).