How do you simplify $\frac{i}{1 + 2 i}$ $i/(1+2i)$ ?

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Answer 1 · 2017-01-21T10:39:34

The answer is $= \frac{2}{5} + \frac{1}{5} i$ $=2/5+1/5i$

When you have a complex number in the denominator, multiply the numerator and denominator by the conjugate of the denominator.

$i^{2} = - 1$ $i^2=-1$

The conjugate of $(1 + 2 i)$ $(1+2i)$ is $(1 - 2 i)$ $(1-2i)$

$\frac{i}{1 + 2 i} = \frac{i}{(1 + 2 i)} \cdot \frac{(1 - 2 i)}{(1 - 2 i)}$ $i/(1+2i)=i/((1+2i))*((1-2i))/((1-2i))$

$= \frac{i - 2 i^{2}}{1 - 4 i^{2}}$ $=(i-2i^2)/(1-4i^2)$

$= \frac{2 + i}{5}$ $=(2+i)/5$

$= \frac{2}{5} + \frac{1}{5} i$ $=2/5+1/5i$

How do you simplify i1+2ii/(1+2i)?