Question

Simplify 1+2i/2+i +4-i/3+2i

Answer 1

Here is the answer for your question

Answer 2

The correct answer is $\frac{10}{13} -\frac{24i}{13}$.

Given: $\frac{1-2i}{2+i} +\frac{4-i}{3+2i}$.

To Find: Evaluate the following equation.

Solution:

$\frac{1-2i}{2+i} +\frac{4-i}{3+2i}$

Rationalize both the terms.

= $\frac{(1-2i)(3+2i)+(4-i)(2+i)}{(2+i)(3+2i)}$

= $\frac{3+2i-6i+4+8+4i-2i+1}{6+4i+3i-2}$

= $\frac{3-4i+12+2i+1}{6+7i-2}$

= $\frac{-2i+16}{7i+4}$

Now, rationalize this term also to get final answer.

$\frac{-2i+16}{7i+4}*\frac{4-7i}{4-7i}$

= $\frac{64-112i-8i-14}{16+49}$

= $\frac{50-120i}{65}$

= $\frac{10}{13}-\frac{24i}{13}$

Hence, the correct answer is  $\frac{10}{13}-\frac{24i}{13}$.

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