# Math Help - complex number algebra

1. ## complex number algebra

$-2 + \frac{\sqrt{-100}}{2}$

the correct answer is $-1 + 5i$

here's my work out;

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

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

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

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

2. ## Re: complex number algebra

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

the correct answer is $-1 + 5i$

here's my work out;

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

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

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

Can someone please show me where I have gone wrong? Thank you.
$\frac{\sqrt{-100}}{2} \ne \sqrt{-50}$

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