equal
deleted
inserted
replaced
322 (simp add: power_mult_distrib right_distrib [symmetric] real_sqrt_mult) |
322 (simp add: power_mult_distrib right_distrib [symmetric] real_sqrt_mult) |
323 show "norm (x * y) = norm x * norm y" |
323 show "norm (x * y) = norm x * norm y" |
324 by (induct x, induct y) |
324 by (induct x, induct y) |
325 (simp add: real_sqrt_mult [symmetric] power2_eq_square ring_simps) |
325 (simp add: real_sqrt_mult [symmetric] power2_eq_square ring_simps) |
326 show "sgn x = x /\<^sub>R cmod x" by(simp add: complex_sgn_def) |
326 show "sgn x = x /\<^sub>R cmod x" by(simp add: complex_sgn_def) |
327 qed (* FIXME junk *) (rule refl)+ |
327 qed |
328 |
328 |
329 lemma cmod_unit_one [simp]: "cmod (Complex (cos a) (sin a)) = 1" |
329 lemma cmod_unit_one [simp]: "cmod (Complex (cos a) (sin a)) = 1" |
330 by simp |
330 by simp |
331 |
331 |
332 lemma cmod_complex_polar [simp]: |
332 lemma cmod_complex_polar [simp]: |