Complex Numbers

What is a Complex Number?

• Standard form of a complex number is a+bi

• The a is a Real Number and the bi is an Imaginary Number

• Another example of a Complex Number is -23 - 72i

Multiple Choice

How do you write a complex number?

• a-bi

• a+bi

• ai+b

• ai-b

Multiple Choice

$$\sqrt{-9}$$  

• 3

• -3

• $$9i$$  

• $$3i$$  

Match

Match the following non-real roots with their complex number form: $$a\cdot i$$ where $$a$$ is a real number.

• $$\sqrt[]{-25}$$

• $$\sqrt[]{-36}$$

• $$\sqrt[]{-100}$$

• $$\sqrt[]{-45}$$

• $$\sqrt[]{-\frac{144}{625}}$$

• $$5i$$

• $$6i$$

• $$10i$$

• $$3\sqrt[]{5}\cdot i$$

• $$\frac{12}{25}i$$

Multiple Choice

$$\sqrt{-20}$$  

• $$i\sqrt{20}$$  

• $$2i\sqrt{5}$$  

• $$20i$$  

• $$-20i$$  

Adding Complex Numbers

• When adding complex numbers

  -Add real parts together

  -Add imaginary parts together

Multiple Choice

Find the Sum

3i + 2i

• 5i

• 5i²

• 6i

• -5

Multiple Choice

Add the two complex numbers:

$$\left(5+7i\right)+\left(8+3i\right)$$

• $$12+11i$$

• $$13+10i$$

• $$-2+5i$$

• $$13-10i$$

Multiple Choice

Find the sum.

(5-2i) + (-7+8i)

• -2+6i

• 12+6i

• -35-16i²

• -35 -16i

Subtracting Complex Numbers

• Distribute the negative

• Add real parts together

  Add imaginary parts together

Multiple Choice

Subtract the two complex numbers:

$$\left(14+9i\right)-\left(23+11i\right)$$

• $$-9-20i$$

• $$37+20i$$

• $$-9+20i$$

• $$-9-2i$$

Multiple Choice

Subtract the two complex numbers:

$$\left(-26-18i\right)-\left(42-39i\right)$$

• $$-68-21i$$

• $$-68-57i$$

• $$16+21i$$

• $$-68+21i$$

Multiplying Complex Numbers

Fill in the Blanks

$4i\left(-2-8i\right)$  

Multiple Choice

(2i)(3i)

• 5i

• -5

• 6i

• -6

Multiple Choice

(4-5i)(4+5i)

• 41

• -9

• 41+40i

• -9+40i

Multiple Choice

(3 + 8i)(-2 - i)

• 2-19i

• 2-18i

• 2+20i

• 23-i

Multiple Choice

What letter represents an imaginary number?

• a

• i

• j

• x

Multiple Choice

Which gives the STANDARD FORM for the complex number:

$$15-\sqrt[]{-81}$$

• $$15+9i$$

• $$15-8i$$

• $$15-9i$$

• $$15-9\sqrt[]{-1}$$

Labeling

Label the

REAL part __

and the

IMAGINARY part __

of the complex number.

Drag labels to their correct position on the image

REAL part

IMAGINARY part

Dividing Complex Numbers

I can divide complex numbers using the complex conjugate.

​Complex Conjugates

Fill in the Blanks

What is the complex conjugate of $10-5i$  ?

Fill in the Blanks

What is the complex conjugate of $21+i$  ?

Fill in the Blanks

What is the complex conjugate of $-3i$  ?

​Dividing Complex Numbers