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 [tex]\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}\\\\
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\textit{recall that }i^2=-1\\\\
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\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}[/tex]
