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Popular >

simplify (3+i)/(1+2i)

Solution

simplify

\frac{3 + i}{1 + 2 i}

Solution

1 - i

Solution steps

\frac{3 + i}{1 + 2 i}

Multiply by the conjugate

\frac{1 - 2 i}{1 - 2 i}

= \frac{( 3 + i ) ( 1 - 2 i )}{( 1 + 2 i ) ( 1 - 2 i )}

Simplify

\frac{( 3 + i ) ( 1 - 2 i )}{( 1 + 2 i ) ( 1 - 2 i )} : \frac{5 - 5 i}{5}

= \frac{5 - 5 i}{5}

Apply the fraction rule:

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

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

Simplify

\frac{5}{5} + \frac{- 5}{5} i : 1 - i

= 1 - i

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expand (1+p)(3-2p)(2+2p)expand

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Frequently Asked Questions (FAQ)

What is (3+i)/(1+2i) ?
The solution to (3+i)/(1+2i) is 1-i