Power of Complex Modulus equals Complex Modulus of Power/Examples/(1+i)^4

Example of Power of Complex Modulus equals Complex Modulus of Power

$\left\vert{\left({1 + i}\right)^4}\right\rvert = 4$

Proof

\(\ds \left\vert{1 + i}\right\rvert\)

\(=\)

\(\ds \sqrt 2\)

Examples of Complex Modulus: $1 + i$

\(\ds \leadsto \ \ \)

\(\ds \left\lvert{\left({1 + i}\right)^4}\right\rvert\)

\(=\)

\(\ds \left({\sqrt 2}\right)^4\)

Power of Complex Modulus equals Complex Modulus of Power

\(\ds \)

\(=\)

\(\ds 4\)

$\blacksquare$

Sources

• 1960: Walter Ledermann: Complex Numbers ... (previous) ... (next): $\S 1.2$. The Algebraic Theory: Examples