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2 years ago

2. Describe how to use the conjugate to divide 2 − i by 3 + 2i, and then find the quotient.

Mathematics

1 answer:

DaniilM [7]2 years ago

7 0

Answer:

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

Step-by-step explanation:

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

Multiply and divide by the conjugate.

The conjugate is the denominator with the sign of the complex number the opposite of the denominator.

$\frac{2-i}{3+2i}\frac{3-2i}{3-2i}\\ =\frac{2\times (3-2i)-i\times (3-2i)}{3^2-(2i)^2}\\ =\frac{6-4i-3i+2i^2}{9+4}\\ =\frac{4-7i}{13}\\ =\frac{4}{13}-\frac{7}{13}i$

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

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