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This lesson introduces the Argand diagram, which provides a geometric representation of complex numbers. Visualising complex numbers as points (or vectors) in a plane is a powerful tool that connects algebra with geometry and opens the door to understanding modulus, argument, and loci.
An Argand diagram is a Cartesian plane where:
The complex number z=a+bi is represented by the point (a,b) or equivalently by the position vector from the origin to (a,b).
| Complex number | Point on Argand diagram |
|---|---|
| 3+2i | (3,2) |
| −1+4i | (−1,4) |
| 5 | (5,0) |
| −3i | (0,−3) |
| 0 | (0,0) |
Key Point: Real numbers lie on the real axis, purely imaginary numbers lie on the imaginary axis.
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