Original heading: 3 units East, 4 units North = 3 + 4i Rotate counter-clockwise by 45 degrees = multiply by 1 + i If we multiply them together we get: (3 + 4i) · (1 + i) = 3 + 4i + 3i + 4i2 = 3−4 + 7i = −1 + 7i So our new orientation is 1 unit West (-1 East), and 7 units North,
Example calculation of complex numbers
