Question

divide.
\\(\frac{4 - 2i}{2i}\\)
write your answer as a complex number in standard form.

Explanation:

Step1: Multiply numerator and denominator by \(i\)

To simplify the fraction \(\frac{4 - 2i}{2i}\), we multiply the numerator and the denominator by \(i\) (the conjugate of the denominator's complex part, here the denominator is \(2i\), and multiplying by \(i\) will help eliminate the \(i\) in the denominator). So we have:

$$ \frac{(4 - 2i)\times i}{2i\times i} $$

Step2: Expand the numerator and denominator

First, expand the numerator: \((4 - 2i)\times i = 4i-2i^{2}\).
Then, expand the denominator: \(2i\times i = 2i^{2}\).
We know that \(i^{2}=- 1\), so substitute \(i^{2}=-1\) into the numerator and denominator:
Numerator: \(4i-2\times(-1)=4i + 2\)
Denominator: \(2\times(-1)=-2\)
So now our fraction becomes \(\frac{4i + 2}{-2}\)

Step3: Simplify the fraction

We can split the fraction: \(\frac{4i+2}{-2}=\frac{4i}{-2}+\frac{2}{-2}\)
Simplify each term: \(\frac{4i}{-2}=-2i\) and \(\frac{2}{-2}=-1\)
So the expression simplifies to \(-1-2i\)

Answer:

\(-1 - 2i\)