Question

The conjugate of $(2+i)/(3+i)$ in the form of $a+ib$ is

• A. $13/2+i\left(15/2\right)$
• B. $7/10+i(-1/10)$
• C. $13/10+i(-15/2)$
• D. $13/10+i\left(9/10\right)$

Answer 1

Answer: (B)

$7/10+i(-1/10)$

$\frac{2+i}{3+i}=\frac{(2+i)(3-i)}{(3+i)(3-i)}=\frac{6+3i-2i-i^2}{9-i^2}$

$=\frac{7+i}{10}=\frac{7}{10}+i\frac{1}{10}$

$\therefore$ Conjugate is $\left(\frac{7}{10}\right)-i\left(\frac{1}{10}\right)$