# Math Help - Need Help, complex

1. ## Need Help, complex

If a =2 +i then in the form of a+bi what does a^-1 equal

2. Originally Posted by Rimas
If a =2 +i then in the form of a+bi what does a^-1 equal
It means the multiplicative inverse,

$\frac{1}{2+i}\cdot \frac{2-i}{2-i}=\frac{2-i}{4+1}=\frac{2}{5}-i\frac{1}{5}$

3. What?

4. Originally Posted by Rimas
What?
I multiplied by the "conjugate" to clear the denominator from imaginary numbers. Note, I multiplied both the numerator and denominator.

The meaning of $a^{-1}$ is definied as the inverse, meaning,
$\frac{1}{2+i}$

5. This is one of my favorite questions.
The multiplicative inverse of a complex number z is:
$z^{ - 1} = \frac{{\overline z }}{{\left| z \right|^2 }}.$

Of course $z\not = 0+0i$