The Argand diagram: modulus, argument and turning
Read complex numbers as points on the Argand diagram, find their modulus and argument, reflect them in the real axis and multiply by turning and stretching.
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Guide
On the Argand diagram the real part goes across and the imaginary part goes up. The conjugate of a + bi is a − bi: its mirror image in the real axis.
The modulus |z| is the distance from the middle to the point, found with Pythagoras: |a + bi| = √(a2 + b2). The argument is the angle from the positive real axis, measured anticlockwise, so look at which quadrant the point is in.
To multiply two complex numbers, multiply their moduli and add their arguments. Multiplying by i adds 90°: a quarter turn anticlockwise.