First Principles AI

Accedmychevron_right11thchevron_rightmathchevron_rightComplex Numberschevron_rightExercise 1.1

Theory

For z = a + bi:

TEXT

Re(z) = a
Im(z) = b
z\u0304 = a - bi
|z|^2 = a^2 + b^2 = z z\u0304

Also:

TEXT

(z + z\u0304)/2 = a
(z - z\u0304)/(2i) = b