Question

What is the answer for 4i over 3+7i

Answer 1

Answer:

see explanation

Step-by-step explanation:

given $\frac{4i}{3+7i}$

To rationalise multiply the numerator/denominator by the conjugate of the denominator

the conjugate of 3 + 7i is 3 - 7i, hence

$\frac{4i(3-7i)}{(3+7i)(3-7i)}$

distribute the numerator/denominator

= $\frac{12i-28i^2}{9-49i^2}$

[ note that i² = - 1 ]

= $\frac{12i+28}{9+49}$

= $\frac{28+12i}{58}$

= $\frac{28}{58}$ + $\frac{12}{58}$ i

= $\frac{14}{29}$ + $\frac{6}{29}$ i ← in standard form