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Popular >

simplify (1+9i)/(1+i)

Solution

simplify

\frac{1 + 9 i}{1 + i}

Solution

5 + 4 i

Solution steps

\frac{1 + 9 i}{1 + i}

Multiply by the conjugate

\frac{1 - i}{1 - i}

= \frac{( 1 + 9 i ) ( 1 - i )}{( 1 + i ) ( 1 - i )}

Simplify

\frac{( 1 + 9 i ) ( 1 - i )}{( 1 + i ) ( 1 - i )} : \frac{10 + 8 i}{2}

= \frac{10 + 8 i}{2}

Apply the fraction rule:

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

= \frac{10}{2} + \frac{8}{2} i

Simplify

\frac{10}{2} + \frac{8}{2} i : 5 + 4 i

= 5 + 4 i

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Frequently Asked Questions (FAQ)

What is (1+9i)/(1+i) ?
The solution to (1+9i)/(1+i) is 5+4i