Question

find the real part, imaginary part, magnitude, and phase of the following complex number: (1+i)/(2+i)

I have an answer but I have no idea if it is correct

Answer 1

(1+i)/(2+i)
multiply and divide by denominator
(1+i)/(2+i)x(2-i)/(2-i)
(1+i)(2-i)/(2+i)(2-i)
(1-i+2i+1)/(4+1)
(2+i)/5
2/5 +i/5
real part = 2/5 imag part = 1/5

Answer 2

sorry its
multiply and divide by the conjugate of denominator

Answer 3

Yes thank you very much, that is what I got as well for the separation. So then magnitude would be: sqrt{[(3/5)+(1/5)]^2}?

Answer 4

yes exactly

Answer 5

and then phase would be the angle of the vector with respect to a "real" axis? I got arctan(1/3)

Answer 6

its arctan(1/2)

Answer 7

yes you are right man i did a mistake sorry its 3

Answer 8

Oh ok
Thank you very much for your time and your help rizwan_uet!

Answer 9

you are welcome

Answer 10

\[\frac{1+i}{2+i} = \frac{(1+i)(2-i)}{(2+i)(2-i)} = \frac{2-i+2i-i^2}{4-i^2}=\frac{3+i}{5} = 3/5 + i/5\]So real part = a = 3/5, imaginary part = b = 1/5.
\[z = \sqrt{a^2+b^2} = \sqrt{(3/5)^2+(1/5)^2} = \sqrt{2/5}\]
\[\theta = \tan^{-1}{(b/a)} = \tan^{-1}{((1/5)/(3/5))} = \tan^{-1}{(1/3)}\]