What is (2i)/(2+i)+5/(2-i) ?

The solution to (2i)/(2+i)+5/(2-i) is 12/5+9/5 i

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simplify (2i)/(2+i)+5/(2-i)

simplify

\frac{2 i}{2 + i} + \frac{5}{2 - i}

\frac{12}{5} + \frac{9}{5} i

Solution steps

\frac{2 i}{2 + i} + \frac{5}{2 - i}

\frac{2 i}{2 + i} = \frac{4 i + 2}{5}

\frac{5}{2 - i} = \frac{10 + 5 i}{5}

= \frac{4 i + 2}{5} + \frac{10 + 5 i}{5}

Join

\frac{4 i + 2}{5} + \frac{10 + 5 i}{5} : \frac{9 i + 12}{5}

= \frac{9 i + 12}{5}

Rewrite in standard complex form:

\frac{12}{5} + \frac{9}{5} i

= \frac{12}{5} + \frac{9}{5} i

56 \cdot \frac{1}{6} 216

3^{3} \cdot 3^{2}

4 x^{2} + 5 x + 3 = 0

6 lo g_{8} (4)

9 x^{2} + 4 x - 16 = 0