Write the expression as a complex number in standard form. 3-3i/4i
I'm not sure about this problem, but I think the answer is -3/4i-3/4. Could anyone help me please?
I guess you mean:
(3-3i)/4i
or
(3/4)(1/i -i/i)
so the real questions are:
What is 1/i and what is i/i
first one:
1/i * i/i = i/-1 = -i
second one:
i/i = 1
so we have:
(3/4)(-i - 1)
or
-3/4 - (3/4)i
so I agree except for the trivial point that that standard form is a + b i not b i + a
Okay, thank you for your help! I will change the order of my answer.
To simplify the expression (3 - 3i) / (4i), we can multiply the numerator and denominator by the conjugate of the denominator.
The conjugate of 4i is -4i.
So, multiplying the numerator and denominator by -4i gives us:
[(3 - 3i) / (4i)] * [-4i / -4i]
Simplifying the numerator:
= (3 - 3i) * -4i
= -12i + 12i^2
(remember that i^2 = -1)
= -12i - 12
Simplifying the denominator:
= 4i * -4i
= -16i^2
= -16(-1)
= 16
Therefore, the simplified expression is:
(-12i - 12) / 16
= -12i/16 - 12/16
Simplifying further:
= (-3i/4) - (3/4)
= -3/4 - (3/4)i
Hence, the expression (3 - 3i) / (4i) simplifies to -3/4 - (3/4)i in standard form.
To write the expression (3 - 3i) / 4i as a complex number in standard form, we need to simplify the division first.
To divide complex numbers, we multiply both the numerator and denominator by the conjugate of the denominator. The conjugate of 4i is -4i.
So, we have:
(3 - 3i) / 4i = ((3 - 3i) * (-4i)) / (4i * (-4i))
Multiplying the numerator and denominator by -4i, as well as expanding the denominator, we get:
= (-12i + 12i^2) / (-16i^2)
Now, we simplify the numerator:
12i^2 = 12(-1) (since i^2 = -1)
= -12
And simplify the denominator:
i^2 = -1
Therefore, we have:
= (-12i - 12) / (-16(-1))
= (-12i - 12) / 16
= (-3i - 3) / 4
So, the expression (3 - 3i) / 4i in standard form is (-3i - 3) / 4.