Theorem imcji

Description: Imaginary part of a complex conjugate. (Contributed by NM, 2-Oct-1999)

	Ref	Expression
Hypothesis	recl.1	⊢ 𝐴 ∈ ℂ
Assertion	imcji	⊢ ( ℑ ‘ ( ∗ ‘ 𝐴 ) ) = - ( ℑ ‘ 𝐴 )

Proof

Step	Hyp	Ref	Expression
1		recl.1	⊢ 𝐴 ∈ ℂ
2		imcj	⊢ ( 𝐴 ∈ ℂ → ( ℑ ‘ ( ∗ ‘ 𝐴 ) ) = - ( ℑ ‘ 𝐴 ) )
3	1 2	ax-mp	⊢ ( ℑ ‘ ( ∗ ‘ 𝐴 ) ) = - ( ℑ ‘ 𝐴 )