(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
(2-3i)(5i) over 2+3i
Please help!! I do not understand this.
= 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
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
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: