Solve any maths problem

Step by step

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

   Read off the real and imaginary parts.

2. |z| = \sqrt{-1^2 + 1^2} = \sqrt{2} \approx 1.4142

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

3. \theta = \arg z = \frac{3 \pi}{4} \approx 2.3562

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

4. z = \sqrt{2}\left(\cos \frac{3 \pi}{4} + i\sin \frac{3 \pi}{4}\right) = \sqrt{2} e^{i \frac{3 \pi}{4}}

   Polar and exponential forms (Euler).