Question

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

Answer 1

see explanation

Explanation:

given
`(4i)/(3+7i)`

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

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

`(4i(3-7i))/((3+7i)(3-7i))`

distribute the numerator/denominator

=
`(12i-28i^2)/(9-49i^2)`

[ note that i² = - 1 ]

=
`(12i+28)/(9+49)`

=
`(28+12i)/(58)`

=
`(28)/(58)` +
`(12)/(58)` i

=
`(14)/(29)` +
`(6)/(29)` i ← in standard form