Question

Simplify the given expression below 2 over 2+5i

Answer 1

Well, you'd do the same as the previous one, use the conjugate of the denominator

$\bf \cfrac{2}{2+5i}\cdot \cfrac{2-5i}{2-5i}\implies \cfrac{4-10i}{(2+5i)(2-5i)}\implies \cfrac{4-10i}{2^2-(5i)^2} \\\\\\ \cfrac{4-10i}{4-(5^2i^2)}\implies \cfrac{4-10i}{4-(25\cdot -1)}\implies \cfrac{4-10i}{4+25}\implies \cfrac{4-10i}{29} \\\\\\ \textit{and then you distribute the denominator} \\\\\\ \cfrac{4}{29}+\cfrac{10}{29}i$