Question

Simplifyalt=" \frac{4}{2 + i} " align="absmiddle" class="latex-formula">

Answer 1

Hey! Apologies that I can’t make this look nice because I’m on mobile.

To simplify this, we can multiply the denominator by its conjugate. For a imaginary function (a+bi), its conjugate would be (a-bi), so we can apply that here to multiply both sides by (2-i)/(2-i). This works because it simplifies to one. Then, we have our fraction as 4*(2-i)/((2-i)(2+i))=(8-4i)/(4-i^2)=(8-4i)/5

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