Answer:
see explanation
Step-by-step explanation:
given [tex]\frac{4i}{3+7i}[/tex]
To rationalise multiply the numerator/denominator by the conjugate of the denominator
the conjugate of 3 + 7i is 3 - 7i, hence
[tex]\frac{4i(3-7i)}{(3+7i)(3-7i)}[/tex]
distribute the numerator/denominator
= [tex]\frac{12i-28i^2}{9-49i^2}[/tex]
[ note that i² = - 1 ]
= [tex]\frac{12i+28}{9+49}[/tex]
= [tex]\frac{28+12i}{58}[/tex]
= [tex]\frac{28}{58}[/tex] + [tex]\frac{12}{58}[/tex] i
= [tex]\frac{14}{29}[/tex] + [tex]\frac{6}{29}[/tex] i ← in standard form
