Megoldani a matematikai problémákat

Lépésről lépésre

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).