# Need Help, complex

• October 23rd 2006, 04:38 PM
Rimas
Need Help, complex
If a =2 +i then in the form of a+bi what does a^-1 equal
• October 23rd 2006, 04:59 PM
ThePerfectHacker
Quote:

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,

$\frac{1}{2+i}\cdot \frac{2-i}{2-i}=\frac{2-i}{4+1}=\frac{2}{5}-i\frac{1}{5}$
• October 24th 2006, 02:45 PM
Rimas
What?
• October 24th 2006, 04:27 PM
ThePerfectHacker
Quote:

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,
$\frac{1}{2+i}$
• October 24th 2006, 04:36 PM
Plato
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 $z\not = 0+0i$