1

I was wondering if this property of complex numbers is true:

$(a^* \times b)^*=(a\times b^*) $

$a^*$ is the complex conjugate of a

If anyone could tell me where I can find more about the properties of complex numbers, it would be helpful.

Do complex numbers follow all the same rules as normal numbers when it comes to addition, subtraction, multiplication and division?

J. W. Tanner
  • 60,406
PhysicsQuestion
  • 131

1 Answers1

0

The product of conjugates is the conjugate of the product,

and conjugating a complex number twice gives the original number,

so indeed $(a^\ast\times b)^\ast=(a^\ast)^\ast\times b^\ast=a\times b^\ast$.

Complex numbers follow the commutative, associative, and distributive rules, like real numbers.

J. W. Tanner
  • 60,406