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stich3 [128]
3 years ago
12

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

Mathematics
1 answer:
DaniilM [7]3 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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