# complex number algebra

• Mar 15th 2012, 02:06 PM
Tweety
complex number algebra
$\displaystyle -2 + \frac{\sqrt{-100}}{2}$

the correct answer is $\displaystyle -1 + 5i$

here's my work out;

$\displaystyle -1 + {\sqrt{-50}$ =
$\displaystyle -1 + \sqrt{50} \times \sqrt{-1}$ =

$\displaystyle -1 + \sqrt{25} \times \sqrt{2} i$

$\displaystyle -1 + 5\sqrt{2}i$

Can someone please show me where I have gone wrong? Thank you.
• Mar 15th 2012, 02:26 PM
skeeter
Re: complex number algebra
Quote:

Originally Posted by Tweety
$\displaystyle -2 + \frac{\sqrt{-100}}{2}$

the correct answer is $\displaystyle -1 + 5i$

here's my work out;

$\displaystyle -1 + {\sqrt{-50}$ =
$\displaystyle -1 + \sqrt{50} \times \sqrt{-1}$ =

$\displaystyle -1 + \sqrt{25} \times \sqrt{2} i$

$\displaystyle -1 + 5\sqrt{2}i$

Can someone please show me where I have gone wrong? Thank you.

$\displaystyle \frac{\sqrt{-100}}{2} \ne \sqrt{-50}$

$\displaystyle \frac{\sqrt{-100}}{2} = \frac{\sqrt{100} \cdot \sqrt{-1}}{2} = \frac{10i}{2} = 5i$