What is (26+28i)/(2+i) ?

The solution to (26+28i)/(2+i) is 16+6i

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simplify (26+28i)/(2+i)

simplify

\frac{26 + 28 i}{2 + i}

16 + 6 i

Solution steps

\frac{26 + 28 i}{2 + i}

Multiply by the conjugate

\frac{2 - i}{2 - i}

= \frac{( 26 + 28 i ) ( 2 - i )}{( 2 + i ) ( 2 - i )}

Simplify

\frac{( 26 + 28 i ) ( 2 - i )}{( 2 + i ) ( 2 - i )} : \frac{80 + 30 i}{5}

= \frac{80 + 30 i}{5}

Apply the fraction rule:

\frac{a + bi}{c} = \frac{a}{c} + \frac{b}{c} i

= \frac{80}{5} + \frac{30}{5} i

Simplify

\frac{80}{5} + \frac{30}{5} i : 16 + 6 i

= 16 + 6 i

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