Simplify (4-2i)/(3+i)

To simplify the expression \(\frac{4-2i}{3+i}\), we can multiply both the numerator and denominator by the conjugate of the denominator, which is \(3-i\). This will eliminate the complex number in the denominator.

So, we have:

\[ \frac{4-2i}{3+i} = \frac{(4-2i)(3-i)}{(3+i)(3-i)} = \frac{12 - 4i - 6i + 2i^2}{3^2 - i^2} = \\ = \frac{12 - 10i -2}{9 + 1} = \frac{10 - 10i}{10} = 1 - i\]

Therefore, \(\frac{4-2i}{3+i}\) simplifies to \(1 - i\).

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Published: 2023-05-10 02:37:39
Updated: 2023-05-10 02:45:55