I have to rationalize the denominator of 2+3i/1+2i. I multiplyed this expression by 1-2i/1-2i, resulting in 2+4i+3i+-6i^2/1+-2i+2i+-4i^2. It then became 2+2i+3i+6/1-1+2i+3. Is this right? Thanks!

Question

I have to rationalize the denominator of 2+3i/1+2i.  I multiplyed this expression by 1-2i/1-2i, resulting in 2+4i+3i+-6i^2/1+-2i+2i+-4i^2.  It then became 2+2i+3i+6/1-1+2i+3.  Is this right? Thanks!

Reiny · Answer

After multiplying I got (2 - 4i + 3i - 6i^2)/(1 - 4i^2) = 2 -i + 6)/(1 + 4) = 8-i)/5