Lesson 2.4 Complex Numbers

​Lesson 2.4 Complex Numbers

By Ruben Gonzales

Multiple Choice

Example 1. Adding and Subtracting Complex Numbers.

$$a.\ \ \left(4+7i\right)+\left(1-6i\right)$$

• $$5i$$

• $$5+i$$

• $$2-i$$

• $$7+3i$$

Multiple Choice

b. $$\left(1+2i\right)-\left(4+2i\right)$$

• $$-3$$

• $$5+4i$$

• $$11-2i$$

• $$-5$$

Multiple Choice

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

• $$-1-2i$$

• $$2+3i$$

• $$-5i$$

• $$-7i$$

Multiple Choice

d. $$\left(3+2i\right)+\left(4-i\right)-\left(7+i\right)$$

• $$5+2i$$

• $$-2i$$

• $$2i$$

• $$0$$

Multiple Choice

Multiplying Complex Numbers

a. $$4\left(-2+3i\right)$$

• $$-8+12i$$

• $$-10+15i$$

• $$3+2i$$

• $$8-7i$$

Multiple Choice

b. $$\left(2-i\right)\left(4+3i\right)$$

• $$18i$$

• $$2-i$$

• $$11+2i$$

• $$5-10i$$

Multiple Choice

c. $$\left(3+2i\right)\left(3-2i\right)$$

• $$-7+10i$$

• $$17i$$

• $$13$$

• $$2+10i$$

Multiple Choice

d. $$\left(3+2i\right)^2$$

• $$5+12i$$

• $$-2+8i$$

• $$-17i$$

• $$10i$$

Multiple Choice

What is the conjuagate of the given complex number?

a. $$1+i$$

• $$-1+i$$

• $$1-i$$

• $$-1-i$$

Multiple Choice

What is the conjuagate of the given complex number?

b. $$4-3i$$

• $$4+3i$$

• $$-4-3i$$

• $$-4+3i$$

Multiple Choice

Mulitply each complex number by its complex conjugate.

$$\left(1+i\right)\left(1-i\right)$$

• $$-10+i$$

• $$3+7i$$

• $$-2i$$

• $$2$$

Multiple Choice

Mulitply each complex number by its complex conjugate.

$$\left(4-3i\right)\left(4+3i\right)$$

• $$-1+5i$$

• $$2+12i$$

• $$25$$

• $$36$$

Multiple Choice

Write the Quotient of the Complex Number in Standard Form.

$$\frac{2+3i}{4-2i}$$

• $$\frac{1}{10}+\frac{4}{5}i$$

• $$\frac{1}{5}-\frac{2}{3}i$$

• $$\frac{7}{5}-\frac{4}{3}i$$

• $$\frac{1}{10}+\frac{3}{4}i$$

Multiple Choice

Write the Quotient of the Complex Number in Standard Form.

$$\frac{4-5i}{1+3i}$$

• $$-\frac{10}{17}+\frac{21}{35}i$$

• $$\frac{7}{8}-\frac{5}{4}i$$

• $$-\frac{15}{2}+\frac{12}{7}i$$

• $$-\frac{11}{10}-\frac{17}{10}i$$

Multiple Choice

Write the complex number in standard form.

$$\sqrt[]{-50}$$

• $$4i\ \sqrt[]{2}$$

• $$4i\ \sqrt[]{2}$$

• $$5i\ \sqrt[]{2}$$

• $$-2i\ \sqrt[]{3}$$

Multiple Choice

Write the complex number in standard form.

$$\sqrt[]{-20}$$

• $$2i\ \sqrt[]{5}$$

• $$-3i\ \sqrt[]{2}$$

• $$i\ \sqrt[]{7}$$

• $$5i\ \sqrt[]{5}$$

Multiple Choice

Write the complex number in standard form.

$$\sqrt[]{-3}\cdot\sqrt[]{-12}$$

• $$-11$$

• $$-6$$

• $$-2$$

• $$0$$

Multiple Choice

Use the Quadratic Formula to find the complex solutions of the given quadratic equation.

$$x=-b\pm\frac{\sqrt[]{b^2-4ac}}{2a}$$

$$x^2+4=0$$

• $$x=\pm2i$$

• $$x=\pm7i$$

• $$x=\pm5$$

• $$x=14i$$

Multiple Choice

Use the Quadratic Formula to find the complex solutions of the given quadratic equation.

$$x=-b\pm\frac{\sqrt[]{b^2-4ac}}{2a}$$

$$3x^2-2x+5=0$$

• $$-\frac{8}{3}\pm\frac{\sqrt[]{24}}{3}$$

• $$\frac{2}{3}\pm\frac{\sqrt[]{11}}{3}$$

• $$\frac{5}{3}\pm\frac{\sqrt[]{10}}{3}i$$

• $$\frac{1}{3}\pm\frac{\sqrt[]{14}}{3}i$$