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

Nov 21, 2015

$10 - 6 i$
The conjugate of $a + b$ is $a - b$. Example: the conjugate of $3 x + 6$ is $3 x - 6$.
The complex conjugate is the exact same, except it includes $i$ (the square root of $- 1$). The conjugate of $a + b i$ is $a - b i$. Therefore, the complex conjugate of $10 + 6 i$ is $10 - 6 i$.
Conjugates, especially complex conjugates, can prove very useful. For example, if $10 + 6 i$ were the denominator of a fraction, you could multiply it by $10 - 6 i$ to get $100 - 6 {i}^{2} = 106$. Complex conjugates are a useful way to clear out the complex $i$ from a denominator or other inopportune place.