Quiz about Lesson 4-8: Complex Numbers

Question 1

How do you write the number $$\sqrt[]{-12}$$ by using the imaginary unit $$i$$

Accepted Answer

$$2i\ \sqrt[]{3}$$

Answer

$$12i$$

Answer

$$i\ \sqrt[]{12}$$

Answer

$$3i\ \sqrt[]{2}$$

Question 2

How do you write the number $$\sqrt[]{-25}$$

Accepted Answer

$$5i$$

Answer

$$i\ \sqrt[]{25}$$

Answer

$$\pm5i$$

Answer

$$-5$$

Question 3

How do you write the number $$\sqrt[]{-7}$$ by using the imaginary unit?

Accepted Answer

$$i\ \sqrt[]{7}$$

Answer

$$-\ \sqrt[]{7}$$

Answer

$$7i$$

Answer

$$-i\ \sqrt[]{7}$$

Question 4

What is the absolute value of $$5-i$$

Accepted Answer

$$\sqrt[]{26}$$

Answer

5-i

Answer

5+i

Answer

5

Question 5

What is the absolute value of $$-3-2i$$

Accepted Answer

$$\sqrt[]{13}$$

Answer

$$\sqrt[]{5}$$

Answer

$$\sqrt[]{11}$$

Answer

$$5$$

Question 6

What is the sum or difference

$$\left(7-2i\right)+\left(-3+i\right)$$

Accepted Answer

4-i

Answer

10-3i

Answer

5-3i

Answer

2+i

Question 7

What is each sum or difference

$$\left(1+5i\right)-\left(3-2i\right)$$

Accepted Answer

-2+7i

Answer

8-9i

Answer

5-7i

Answer

4+7i

Question 8

What is each sum or difference

$$\left(8+6i\right)-\left(8-6i\right)$$

Accepted Answer

12i

Answer

16i

Answer

10i

Answer

14i

Question 9

What is the sum or difference

$$\left(-3+9i\right)+\left(3+9i\right)$$

Accepted Answer

18i

Answer

6+18i

Answer

6-9i

Answer

9+18i

Question 10

What is the product of $$\left(7i\right)\left(3i\right)$$

Accepted Answer

$$-21$$

Answer

$$21i$$

Answer

$$10$$

Answer

$$21$$

Question 11

What is the product of $$\left(2-3i\right)\left(4+5i\right)$$

Accepted Answer

23 - 2i

Answer

10 - 7i

Answer

8 + 15i

Answer

6 - 11i

Question 12

What is the product $$\left(-4+5i\right)\left(-4-5i\right)$$

Accepted Answer

41

Answer

-41

Answer

20i

Answer

16-20i

Question 13

What is the quotient of $$\frac{5-2i}{3+4i}$$

Accepted Answer

$$\frac{7}{25}-\frac{26}{25}i$$

Answer

$$\frac{7}{25}+\frac{26}{25}i$$

Answer

$$-\frac{7}{25}-\frac{26}{25}i$$

Answer

$$-\frac{1}{6}-\frac{2}{3}i$$

Question 14

What is the quotient of $$\frac{4-i}{6i}$$

Accepted Answer

$$-\frac{1}{6}-\frac{2}{3}i$$

Answer

$$-\frac{1}{6}+\frac{2}{3}i$$

Answer

$$\frac{1}{6}+\frac{2}{3}i$$

Answer

$$6+\frac{3}{2}i$$

Question 15

What is the quotient of $$\frac{8-7i}{8+7i}$$

Accepted Answer

$$\frac{15}{113}-\frac{112}{113}i$$

Answer

$$-\frac{15}{113}+\frac{112}{113}i$$

Answer

$$\frac{113}{15}-\frac{113}{112}i$$

Answer

$$2$$

Question 16

What is the factored form of the expression $$5x^2+20$$ . Factor out as far as you are able to.

Accepted Answer

$$5\left(x+2i\right)\left(x-2i\right)$$

Answer

$$25\left(x^2+16\right)$$

Answer

$$5\left(x^2+4\right)$$

Answer

$$\left(x+2i\right)\left(x-2i\right)$$

Question 17

What is the factored for of the expression $$x^2+81$$

Accepted Answer

(x+9i)(x-9i)

Answer

(x+7)(x-7)

Answer

(x+9)(x-9)

Answer

(x+8)(x-8)

Question 18

What are the solutions to the equation $$3x^2-x+2=0$$

Accepted Answer

$$\frac{1}{6}\pm\frac{i\ \sqrt[]{23}}{6}$$

Answer

4

Answer

$$\frac{1}{6}\pm\frac{\sqrt[]{-23}}{6}$$

Answer

$$-\frac{1}{6}-\frac{i\ \sqrt[]{23}}{6}$$

Question 19

What is the solutions of the equation $$x^2-4x+5=0$$

Accepted Answer

$$2\pm i$$

Answer

$$-2-i$$

Answer

$$-2+i$$

Answer

There are no real or imaginary solutions.

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