Magnitude of Projection of Complex Number on Another

Theorem

Let $z_1$ and $z_2$ denote complex numbers in vector form.

Let $\map {\pr_1} {z_1, z_2}$ denote the projection of $z_1$ on $z_2$.

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Then:

$\cmod {\map {\pr_1} {z_1, z_2} } = \dfrac {\cmod {z_1 \circ z_2} } {\cmod {z_2} }$

where:

$z_1 \circ z_2$ denotes complex dot product

$\cmod {z_2}$ denotes complex modulus.

Proof

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Sources

• 1981: Murray R. Spiegel: Theory and Problems of Complex Variables (SI ed.) ... (previous) ... (next): $1$: Complex Numbers: Dot and Cross Product: $3.$