Perform the operation and write the result in standard form.

(2-3i)(5i) over 2+3i

= 5i(2-3i)/(2+3i)
multiply top and bottom by 2-3i

= 5i(4 - 12i + 9i^2)/(4-9i^2)
= 5i(-13 - 12i)/13
= (-65i - 60i^2)/13
= (60 - 65i)/13

or 60/13 - 5i if by standard form you mean a + bi

ok, Kim ,I messed up in the arithmetic

but, if you understand what I did, you should be able to fix it yourself.

hint: the error is from
= 5i(4 - 12i + 9i^2)/(4-9i^2) to
= 5i(-13 - 12i)/13

YOU SHOULD KNOW HOW TO DO THIS!

To perform the operation and write the result in standard form, we need to simplify the expression using the rules of complex numbers.

The expression is: (2 - 3i)(5i) / (2 + 3i)

To simplify this expression, we can use the distributive property of multiplication over addition:

(2 - 3i)(5i) = 2(5i) - 3i(5i) = 10i - 15i^2

Next, we need to simplify i^2. Remember that i is defined as the square root of -1, so i^2 is equal to -1.

Therefore, i^2 = -1

Substituting this back into our expression:

10i - 15i^2 = 10i - 15(-1) = 10i + 15

Now we have simplified the numerator.

Next, let's simplify the denominator, which is 2 + 3i.

To rationalize the denominator, we need to multiply the numerator and the denominator by the conjugate of the denominator. The conjugate of 2 + 3i is 2 - 3i.

Multiplying the numerator and the denominator by the conjugate:

(2 - 3i)(2 - 3i) = 4 - 6i - 6i + 9i^2
= 4 - 12i - 9
= -5 - 12i

Now we have both the simplified numerator and denominator.

The final step is to divide the numerator by the denominator:

(10i + 15) / (-5 - 12i)

To divide complex numbers, we multiply the numerator and the denominator by the conjugate of the denominator:

((10i + 15)(-5 + 12i)) / ((-5 - 12i)(-5 + 12i))

Simplifying this expression will give us the final result in standard form. I will calculate it for you: