Question

What is the complex conjugate of number 12+5i?

Answer 1

The complex conjugate of `(12+5i)` is `(12-5i)`

Explanation:

The complex conjugate is the value you need to multiply a given complex number by

• to eradicate the imaginary component
• using the concept of difference of squares:
  `color(white)("XXXX")` `(a^2-b^2) = (a+b)(a-b)`
  `color(white)("XXXX")`or, for complex numbers:
  `color(white)("XXXX")` `(a^2+b^2) = (a^2-(bi)^2) = (a+bi)(a-bi)`

That is
`color(white)("XXXX")` `(a+bi)` and `(a-bi)` are complex conjugates of each other.