How to find value with a number line

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Algebra › How to find value with a number line

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

The answer must be in standard form.

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

CORRECT

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

$\frac{1}{5i}$

$\frac{2}{3}i$

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 =

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