Theorem absvalsq2i

Description: Square of value of absolute value function. (Contributed by NM, 2-Oct-1999)

	Ref	Expression
Hypothesis	absvalsqi.1	$$⊢A\in ℂ$$
Assertion	absvalsq2i	$$⊢{\left|A\right|}^2={\Re \left(A\right)}^2+{\Im \left(A\right)}^2$$

Proof

Step	Hyp	Ref	Expression
1		absvalsqi.1	$$⊢A\in ℂ$$
2		absvalsq2	$$⊢A\in ℂ\to {\left|A\right|}^2={\Re \left(A\right)}^2+{\Im \left(A\right)}^2$$
3	1 2	ax-mp	$$⊢{\left|A\right|}^2={\Re \left(A\right)}^2+{\Im \left(A\right)}^2$$