Complex Modulus/Examples/z1 + z2/Proof 1
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Example of Complex Modulus
- $\cmod {z_1 + z_2} = \sqrt {10}$
Proof
An illustration of the modulus of the sum of the complex numbers:
- $z_1 = 4 - 3 i$
- $z_2 = -1 + 2 i$
is given below:
The modulus is seen to be the radius of the circle.
$\blacksquare$
Sources
- 1981: Murray R. Spiegel: Theory and Problems of Complex Variables (SI ed.) ... (previous) ... (next): $1$: Complex Numbers: Supplementary Problems: Graphical Representation of Complex Numbers. Vectors: $63 \ \text {(a)}$