Description: Value of the conjugate of a complex number. The value is the real part minus _i times the imaginary part. Definition 10-3.2 of Gleason p. 132. (Contributed by Mario Carneiro, 29-May-2016)
| Ref | Expression | ||
|---|---|---|---|
| Hypothesis | recld.1 | |- ( ph -> A e. CC ) |
|
| Assertion | remimd | |- ( ph -> ( * ` A ) = ( ( Re ` A ) - ( _i x. ( Im ` A ) ) ) ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | recld.1 | |- ( ph -> A e. CC ) |
|
| 2 | remim | |- ( A e. CC -> ( * ` A ) = ( ( Re ` A ) - ( _i x. ( Im ` A ) ) ) ) |
|
| 3 | 1 2 | syl | |- ( ph -> ( * ` A ) = ( ( Re ` A ) - ( _i x. ( Im ` A ) ) ) ) |