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Common Core: High School - Number and Quantity : Complex Conjugate: CCSS.Math.Content.HSN-CN.A.3

Study concepts, example questions & explanations for Common Core: High School - Number and Quantity

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Example Questions

Example Question #83 : High School: Number And Quantity

Simplify.

$\frac{3+2i}{9-6i}$ $\displaystyle \frac{3+2i}{9-6i}$

Possible Answers:

3+3i $\displaystyle 3+3i$

$\frac{5+12i}{39}$ $\displaystyle \frac{5+12i}{39}$

-6+8i $\displaystyle -6+8i$

$\frac{1}{3}$ $\displaystyle \frac{1}{3}$

Correct answer:

$\frac{5+12i}{39}$ $\displaystyle \frac{5+12i}{39}$

Explanation:

$\frac{3+2i}{9-6i}\cdot \frac{9+6i}{9+6i}$ $\displaystyle \frac{3+2i}{9-6i}\cdot \frac{9+6i}{9+6i}$

$=\frac{\left ( 3+2i \right )\left ( 9+6i \right )}{\left ( 9-6i \right )\left ( 9+6i \right )}$ $\displaystyle =\frac{\left ( 3+2i \right )\left ( 9+6i \right )}{\left ( 9-6i \right )\left ( 9+6i \right )}$

$=\frac{27+18i+18i+12i^{2}}{81+54i-54i-36i^{2}}$ $\displaystyle =\frac{27+18i+18i+12i^{2}}{81+54i-54i-36i^{2}}$

$=\frac{27+36i-12}{81+36}$ $\displaystyle =\frac{27+36i-12}{81+36}$

$=\frac{15+36i}{117}$ $\displaystyle =\frac{15+36i}{117}$

$=\frac{3\left ( 5+12i \right )}{3\left ( 39 \right )}$ $\displaystyle =\frac{3\left ( 5+12i \right )}{3\left ( 39 \right )}$

$=\frac{5+12i}{39}$ $\displaystyle =\frac{5+12i}{39}$

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Example Question #11 : Complex Conjugate: Ccss.Math.Content.Hsn Cn.A.3

Simplify.

$\frac{6-4i}{-3i}$ $\displaystyle \frac{6-4i}{-3i}$

Possible Answers:

6-7i $\displaystyle 6-7i$

6-i $\displaystyle 6-i$

-2i $\displaystyle -2i$

$\frac{4+6i}{3}$ $\displaystyle \frac{4+6i}{3}$

Correct answer:

$\frac{4+6i}{3}$ $\displaystyle \frac{4+6i}{3}$

Explanation:

$\frac{6-4i}{-3i}\cdot \frac{3i}{3i}$ $\displaystyle \frac{6-4i}{-3i}\cdot \frac{3i}{3i}$

$\frac{18i-12i^{2}}{-9i^{2}}$ $\displaystyle \frac{18i-12i^{2}}{-9i^{2}}$

$\frac{18i+12}{9}$ $\displaystyle \frac{18i+12}{9}$

$\frac{12+18i}{9}$ $\displaystyle \frac{12+18i}{9}$

$\frac{3\left ( 4+6i \right )}{3\left ( 3 \right )}$ $\displaystyle \frac{3\left ( 4+6i \right )}{3\left ( 3 \right )}$

$\frac{4+6i}{3}$ $\displaystyle \frac{4+6i}{3}$

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Common Core: High School - Number and Quantity : Complex Conjugate: CCSS.Math.Content.HSN-CN.A.3

Study concepts, example questions & explanations for Common Core: High School - Number and Quantity

All Common Core: High School - Number and Quantity Resources

Example Questions

Example Question #83 : High School: Number And Quantity

Example Question #11 : Complex Conjugate: Ccss.Math.Content.Hsn Cn.A.3

All Common Core: High School - Number and Quantity Resources

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