How to find value with a number line - Algebra 1

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Question

Divide: $\frac{2-i}{3+2i}$

The answer must be in standard form.

Answer

Multiply both the numerator and the denominator by the conjugate of the denominator which is which results in

$\frac{\left ( 2-i \right )\left ( 3-2i \right )}{\left ( 3+2i \right )\left ( 3-2i \right )}$

The numerator after simplification give us $6-4i-3i+2i^{2}=6-7i+2i^{2}=4-7i$

The denominator is equal to $3^{2}-4i^{2}=9+4=13$

Hence, the final answer in standard form =

$\frac{4}{13}-\frac{7i}{13}$

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