# How to simplify complex numbers?

I have solved the following expression involving complex numbers by two different methods. However, they yield different results. The expression is $$\frac{1}{1+3j} - \frac{1}{j} + \frac{1}{2}$$

First, by converting denominator of first term to real number by multiplying by conjugate of $1+3j$, $1/j= -j$.

Second, by first taking L.C.M. of $(1+3j)(j)(2)$ and then simplifying.

Rest is different in both cases.....?

• If you're getting two different results, it's likely you're making a small mistake in one (or both!) of your approaches. Please show all your work, and someone should be able to point to where you went wrong. – Barry Cipra Oct 6 '15 at 15:28
• $1/(1+3i)-1/i+1/2=(1-3i)/10+i+1/2=3/5+7i/10$ – ewcz Oct 6 '15 at 15:30