Answer:
Option (2)
Step-by-step explanation:
Given : y = [tex]\frac{x+3}{6-x}[/tex]
If x = 7i
y = [tex]\frac{7i+3}{6-7i}[/tex]
By simplifying denominator of the given rational expression,
y = [tex]\frac{7i+3}{6-7i}\times \frac{6+7i}{6+7i}[/tex]
y = [tex]\frac{(7i+3)(6+7i)}{6^2-(7i)^2}[/tex]
y = [tex]\frac{7i(6+7i)+3(6+7i)}{36-49i^2}[/tex]
y = [tex]\frac{42i+49i^2+18+21i}{36+49}[/tex] [Since, i² = (-1)]
y = [tex]\frac{63i-49+18}{85}[/tex]
y = [tex]\frac{63i-31}{85}[/tex]
y = [tex]-\frac{31}{85}+\frac{63}{85}i[/tex]
Therefore, Option (2) is the correct option.
