1. ## simplify:

simplify:

3/i + 6/(i+2) + i/(i-2)

2. Originally Posted by Mr_Green
simplify:

3/i + 6/(i+2) + i/(i-2)
i is a square root. Thus we wish to get rid of the square roots in the denominators. You do this by multiplying the denominator by the complex conjugate of the denominator.

For example:
$\displaystyle \frac{6}{i+2} = \frac{6}{i+2} \cdot \frac{-i + 2}{-i + 2}$

= $\displaystyle \frac{6(-i+2)}{-i^2 + 4} = \frac{12 - 6i}{1+4} = \frac{12-6i}{5}$

Can you take it from here?

-Dan

3. Originally Posted by topsquark
i is a square root. Thus we wish to get rid of the square roots in the denominators. You do this by multiplying the denominator by the complex conjugate of the denominator.

For example:
$\displaystyle \frac{6}{i+2} = \frac{6}{i+2} \cdot \frac{-i + 2}{-i + 2}$

= $\displaystyle \frac{6(-i+2)}{-i^2 + 4} = \frac{12 - 6i}{1+4} = \frac{12-6i}{5}$

Can you take it from here?

-Dan
$\displaystyle \frac{3}{i} \times \frac{i}{i}=-3i$
$\displaystyle \frac{i}{i-2} \times \frac{i+2}{i+2}=...$