Question

what is the reciprocal of 4i and put it in a+bi form

Answer 1

The reciprocal of a number starts by writing 1 over the number.
Do that first.

Answer 2

To find the reciprocal of a number, all you need to do is write 1 over that number.
Very often, it may be necessary to then simplify. That why the reciprocal of 1/5 is not left as 1 over 1/5, but rather as simply 5.

Answer 3

Now that we have the reciprocal of 4i as 1/(4i), we need to write it in a + bi form.

Answer 4

It is not considered good form to leave a complex number in the denominator.
In order to get rid of the complex number in the denominator, we multiply the numerator and denominator of the fraction by the complex conjugate of the denominator.

Answer 5

Do you know what the complex conjugate of a number is?