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Metamath Proof Explorer
Description: Construct a complex number from its real and imaginary parts.
(Contributed by NM, 1-Oct-1999)
|
|
Ref |
Expression |
|
Hypothesis |
recl.1 |
⊢ 𝐴 ∈ ℂ |
|
Assertion |
replimi |
⊢ 𝐴 = ( ( ℜ ‘ 𝐴 ) + ( i · ( ℑ ‘ 𝐴 ) ) ) |
Proof
| Step |
Hyp |
Ref |
Expression |
| 1 |
|
recl.1 |
⊢ 𝐴 ∈ ℂ |
| 2 |
|
replim |
⊢ ( 𝐴 ∈ ℂ → 𝐴 = ( ( ℜ ‘ 𝐴 ) + ( i · ( ℑ ‘ 𝐴 ) ) ) ) |
| 3 |
1 2
|
ax-mp |
⊢ 𝐴 = ( ( ℜ ‘ 𝐴 ) + ( i · ( ℑ ‘ 𝐴 ) ) ) |