What is (1+2i)/(7+2i) ?

The solution to (1+2i)/(7+2i) is 11/53+12/53 i

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simplify (1+2i)/(7+2i)

simplify

\frac{1 + 2 i}{7 + 2 i}

\frac{11}{53} + \frac{12}{53} i

Solution steps

\frac{1 + 2 i}{7 + 2 i}

Multiply by the conjugate

\frac{7 - 2 i}{7 - 2 i}

= \frac{( 1 + 2 i ) ( 7 - 2 i )}{( 7 + 2 i ) ( 7 - 2 i )}

Simplify

\frac{( 1 + 2 i ) ( 7 - 2 i )}{( 7 + 2 i ) ( 7 - 2 i )} : \frac{11 + 12 i}{53}

= \frac{11 + 12 i}{53}

Rewrite in standard complex form:

\frac{11}{53} + \frac{12}{53} i

= \frac{11}{53} + \frac{12}{53} i

\frac{4}{3} \times 4

2^{0 - 1}

3 \times (- 8)

3 \times 10

1 0^{2} \cdot 1 0^{- 3}