Complex Number Review

Final Exam Review #7

Add, Subtract, Multiply

Complex Numbers

Adding and Subtracting Complex Numbers

Add all the real numbers together

Combine all the imaginary numbers (add coefficients)

Write answer in the form

a + bi

Multiple Choice

Add/Subtract:

(3 + i) + (-8 + 6i) - (-2 + 7i)

• -3 + 14i

• -3

• 3 + 14i

• 7 + 14i

Multiple Choice

Add/Subtract using the proper rules:

-3i + 2 - 4i + 16 - (4 - 8i)

• 22 - 15i

• 14 + i

• 14 - i

• - 22 + 15i

Multiple Choice

Simplify: 
(10+ 15i) - (48 - 30i)

• 58 - 45i
• 58 - 15i
• -38 - 15i
• -38 + 45i

Multiple Choice

$$2\left(3\ +\ 4i\right)-\left(4\ -\ 6i\right)$$  

• $$2\ +\ 14i$$  

• $$10\ +\ 2i$$  

• $$-1\ -2i$$  

• $$-2\ -2i$$  

Multiple Choice

Simplify the expression:
$$\left(5\ +\ 4i\right)\ -\ \left(-1\ -\ 2i\right)$$  

• $$6\ +6i$$  

• $$4\ +\ 2i$$  

• $$6\ -\ 6i$$  

• $$4\ -\ 2i$$  

Multiple Choice

Simplify the expression:
$$\left(5\ +\ 14i\right)\ -\ \left(10\ +\ 2i\right)$$  

• $$5\ -16i$$  

• $$-5\ +\ 16i$$  

• $$5\ -\ 12i$$  

• $$-5\ +\ 12i$$  

Multiple Choice

Simplify the expression:
$$\left(8\ +\ 9i\right)\ +\ \left(4\ -\ 6i\right)$$  

• $$17\ +\ 3i$$  

• $$12\ +\ 3i^2$$  

• $$17\ -2i$$  

• $$12\ +\ 3i$$  

Multiple Choice

Simplify the expression:
$$\left(1\ +\ 5i\right)\ +\ \left(1\ -\ 5i\right)$$  

• $$2\ +\ 10i$$  

• $$2\ +\ 10i^2$$  

• $$2$$  

• $$-8$$  

Multiply Complex Numbers

 $\sqrt{-1}=i\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ i^2=-1$  
Remember that each term in the first group needs to get distributed (multiplied) to each term in the second group.

(3 + i)(2 - i) =
3(2) +  3(-1i) +  1i(2)+ i(-i)  =
6 - 3i + 2i  -  i^2=
6 -1i - (-1) = 6 -1i +1=  

7-1i  or 7 - i

Multiple Choice

Another way to express √-1 is?

• 1

• -1

• i

• 0

Multiple Choice

What does i² = ?

• -1
• √-1
• 1
• -√1

Multiple Choice

(i)(3i)

• -3i
• -3
• 3
• 2i

Multiple Choice

(-4i)(3i)(4i)

• 24
• -48i
• 48i
• 60

Multiple Choice

(-3-i)(6-i)

• -21-7i
• -19-3i
• -15-5i
• -17-9i

Multiple Choice

(7-5i)(7+5i)

• 74
• 75
• 74-1

Multiple Choice

(5-i)(5-i)

• 15-8i
• 36
• 24+10i
• 24-10i