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Common Core: High School - Number and Quantity : The Complex Number System

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

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All Common Core: High School - Number and Quantity Resources

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Example Questions

Example Question #51 : The Complex Number System

Solve.

$4x^{2}+2x+3$

Possible Answers:

$x=-2\pm \sqrt{11}$

$x=\frac{-2\pm i\sqrt{11}}{4}$

$x=\pm 2i$

$x=4\textup{ and }x=-1$

Correct answer:

$x=\frac{-2\pm i\sqrt{11}}{4}$

Explanation:

a=4

b=2

c=3

$x=\frac{-4\pm \sqrt{\left ( 2 \right )^{2}-4\cdot 4\cdot 3}}{2\cdot 4}$

$x=\frac{-4\pm \sqrt{4-48}}{8}$

$x=\frac{-4\pm \sqrt{-44}}{8}$

$x=\frac{-4\pm \sqrt{4\cdot 11\cdot -1}}{8}$

$x=\frac{-4\pm 2i\sqrt{11}}{8}$

$x=\frac{-2\pm i\sqrt{11}}{4}$

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Example Question #51 : The Complex Number System

Solve.

$x^{2}-2x+5$

Possible Answers:

$x=1\pm 2i$

$x=1\pm \sqrt{16}$

$x=1\textup{ and }x=-2$

$x=\pm 2i$

Correct answer:

$x=1\pm 2i$

Explanation:

$x=\frac{-(-2)\pm \sqrt{(-2)^{2}-4\cdot 1\cdot 5}}{2\cdot 1}$

$x=\frac{2\pm \sqrt{4-20}}{2}$

$x=\frac{2\pm \sqrt{-16}}{2}$

$x=\frac{2\pm 4i}{2}$

$x=1\pm 2i$

Report an Error

Example Question #53 : The Complex Number System

Solve.

$a^{2}-6a+13$

Possible Answers:

$a=\pm 3$

$a=3\textup{ and }a=-1$

$a=\pm 4i$

$a=3\pm 2i$

Correct answer:

$a=3\pm 2i$

Explanation:

$a=\frac{-(-6)\pm \sqrt{\left ( -6 \right )^{2}-4\cdot 1\cdot 13}}{2\cdot 1}$

$a=\frac{6\pm \sqrt{36-52}}{2}$

$a=\frac{6\pm \sqrt{-16}}{2}$

$a=\frac{6\pm \sqrt{16\cdot -1}}{2}$

$a=\frac{6\pm 4i}{2}$

$a=3\pm 2i$

Report an Error

Example Question #54 : The Complex Number System

Solve.

$3b^{2}-4b+5$

Possible Answers:

$b=\pm 3$

$b=2\pm i\sqrt{11}$

$b=\pm 4i$

$b=\frac{2\pm i\sqrt{11}}{3}$

Correct answer:

$b=\frac{2\pm i\sqrt{11}}{3}$

Explanation:

Report an Error

Example Question #55 : The Complex Number System

Solve.

$g^{2}-18g+84$

Possible Answers:

$g\pm 3$

$9\pm i\sqrt{3}$

$g=\pm i\sqrt{3}$

$g=\pm 4i$

Correct answer:

$9\pm i\sqrt{3}$

Explanation:

Report an Error

Example Question #56 : The Complex Number System

Solve.

$2m^{2}-8m+25$

Possible Answers:

$m=\pm 4$

$m=\pm 3i$

$m=3\pm i\sqrt{17}$

$m=\frac{4\pm i\sqrt{17}}{2}$

Correct answer:

$m=\frac{4\pm i\sqrt{17}}{2}$

Explanation:

Report an Error

Example Question #57 : The Complex Number System

Solve.

$4a^{2}+25=0$

Possible Answers:

$a=\pm 25$

$a=\pm 5i$

$a=\pm \frac{5}{2}i$

$a=\pm \frac{5}{2}$

Correct answer:

$a=\pm \frac{5}{2}i$

Explanation:

Report an Error

Example Question #58 : The Complex Number System

Solve.

$8z^{2}+72=0$

Possible Answers:

$z=\pm 3$

$z=\sqrt{9}$

$z=\pm 9i$

$z=\pm 3i$

Correct answer:

$z=\pm 3i$

Explanation:

10.

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Example Question #52 : The Complex Number System

Solve.

$2x^{2}+8=0$

Possible Answers:

$x=\pm 2i$

$x=\pm 4$

$x=\pm 2$

$x=\pm 4i$

Correct answer:

$x=\pm 2i$

Explanation:

11.

Report an Error

Example Question #53 : The Complex Number System

Solve.

$10x^{2}+10=0$

Possible Answers:

$x=\pm i$

$x=\pm 10i$

$x=\pm 10$

$x=\pm 1$

Correct answer:

$x=\pm i$

Explanation:

$10\left ( x^{2}+1 \right )=0$

$x^{2}+1=0$

$x^{2}=-1$

$x=\pm \sqrt{-1}$

$x=\pm i$

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All Common Core: High School - Number and Quantity Resources

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Common Core: High School - Number and Quantity : The Complex Number System

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 #51 : The Complex Number System

Example Question #51 : The Complex Number System

Example Question #53 : The Complex Number System

Example Question #54 : The Complex Number System

Example Question #55 : The Complex Number System

Example Question #56 : The Complex Number System

Example Question #57 : The Complex Number System

Example Question #58 : The Complex Number System

Example Question #52 : The Complex Number System

Example Question #53 : The Complex Number System

All Common Core: High School - Number and Quantity Resources

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