Question

I need help in dividing imaginary numbers. The problem is 3+i/5-i. Step by step please!

Answer 1

\[\frac{3+i}{5-i}=\frac{3+i}{5-i}*\frac{5+i}{5+i}=\frac{15+3i+5i+i^2}{25-i^2}=\frac{15+8i-1}{25+1}=\frac{14+8i}{26}=\frac{7}{13}+\frac{4i}{13}\]

Answer 2

the trick with division in complex numbers is that you always multiply the top and bottom by the conjugate of the denominator, then you just multiply everything out on the numerator. On the denominator, notice that you just have the difference of squares.

Answer 3

Oh. I see how you did it. Yeah that makes sense. Thank you! Do you think you could help me with one last problem?

Answer 4

I could try