It's just the xy-plane for complex numbers: An Argand diagram plots complex numbers like points: the real part goes across, the imaginary part goes up.
So z = a + bi is the point (a, b).
Each complex number is a point: a across (Re), b up (Im).
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Distance from 0 — it's Pythagoras: The modulus |z| is the distance from the origin to the point (a, b). Drop a right angle and use Pythagoras:
|z| = √(a² + b²).
|z| is the length of the line from 0 to the point — found with Pythagoras.
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IB-style question — find the modulus
Find |3 + 4i|.
Step by step
- Square the real and imaginary parts and add.
- Work it out.
Final answer
5.