Question

What is the complex conjugate of `10+6i`?

Answer 1

`10-6i`

Explanation:

The conjugate of `a+b` is `a-b`. Example: the conjugate of `3x+6` is `3x-6`.

The complex conjugate is the exact same, except it includes `i` (the square root of `-1`). The conjugate of `a+bi` is `a-bi`. Therefore, the complex conjugate of `10+6i` is `10-6i`.

Conjugates, especially complex conjugates, can prove very useful. For example, if `10+6i` were the denominator of a fraction, you could multiply it by `10-6i` to get `100-6i^2=106`. Complex conjugates are a useful way to clear out the complex `i` from a denominator or other inopportune place.