Theorem cjmulvali

Description: A complex number times its conjugate. (Contributed by NM, 2-Oct-1999)

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

Proof

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