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finlep [7]
3 years ago
6

Simplify the given expression below 2 over 2+5i

Mathematics
1 answer:
mezya [45]3 years ago
8 0
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
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