Question

Write in standard form 2+4i over 1+i

Answer 1

so hmm a conjugate, is pretty much just, the same binomial, but with a different sign in the middle, so, a + b, has a conjugate of a - b
or -a + b, has a conjugate of - a - b, or c - d, has a conjugate of c +d, and so on

anyway, the idea being, to "rationalize" the expression, namely, getting rid of the pesky radical in the denominator

so, we'll multiply the expression by 1, since anything times 1 is just itself

however, bear in mind, that 1, can be a/a, or b/b, or cheese/cheese, or anything/anything

so, we'll multiply the top and bottom of the fraction, by the conjugate of the denominator

anyhow, that said
`\bf \cfrac{2+4i}{1+i}\cdot \cfrac{1-i}{1-i}\implies \cfrac{(2+4i)(1-i)}{(1+i)(1-i)}\implies \cfrac{2-2i+4i-4i^2}{1-i^2}\\\\ -----------------------------\\\\ \textit{recall that }i^2=-1\\\\ -----------------------------\\\\ \cfrac{2-2i+4i-4(-1)}{1-(-1)}\implies \cfrac{2+2i+4}{2}\implies \cfrac{6+2i}{2}\implies \cfrac{6}{2}+\cfrac{2i}{2} \\\\\\ \boxed{3+i}`