Complex numbers: add, subtract, multiply, and divide

Complex numbers: add, subtract, multiply, and divide

by Wilkerny Jeanty

Multiple Choice

Simplify i⁴³

• 1

• i

• -i

• -1

Multiple Choice

Simplify i²⁴

• i

• 1

• -1

• -i

Multiple Choice

What does i² = ?

• -1
• √-1
• 1
• -√1

Multiple Choice

How do you write a complex number?

• a-bi

• a+bi

• ai+b

• ai-b

Multiple Choice

The complex conjugate can be found by...

• Changing the sign of both a and b

• Changing the sign of a

• Changing the sign of b

• Switching the a and b values

Multiple Choice

A complex number can be expressed as a + bi. What does a represent?

• the real part of the complex number

• the imaginary part of the complex number

• depends on the sign of the number

• the square root of the complex number

Multiple Choice

The complex conjugate of 4 + 3i is

• 3 + 4i

• 3 - 4i

• 4 - 3i

• 4 + 3i

Multiple Choice

If you are combining two complex numbers you should

• add all the numbers together then divide by 2

• add only the real numbers and subtract the complex numbers

• add only the complex numbers and subtract the real numbers

• add only the real numbers together and then add only the complex numbers together then stop

Multiple Choice

• A
• B
• C
• D

Multiple Choice

• 5i
• -5i
• 5+i
• -5

Multiple Choice

Add or subtract:

$$\left(2+3i\right)+\left(4-5i\right)+\left(-6+7i\right)$$  

• 2 + 5i

• 5i

• 8 + 2i

• 5

Multiple Choice

Simplify: 
(10+ 15i) - (48 - 30i)

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

Multiple Choice

Simplify $$-\frac{2}{i}$$  

• $$i$$  

• $$-i$$  

• $$4i$$  

• $$2i$$  

Multiple Choice

Simplify $$\frac{3}{16i}$$  

• $$-\frac{3i}{16}$$  

• $$-\frac{3i}{8}$$  

• $$-\frac{i}{4}$$  

• $$-\frac{i}{2}$$  

Multiple Choice

Simplify $$\frac{12}{8i}$$  

• $$-\frac{13i}{8}$$  

• $$-\frac{7i}{4}$$  

• $$-\frac{3i}{2}$$  

• $$\frac{3i}{7}$$  

Multiple Choice

Simplify $$\frac{3}{12-2i}$$  

• $$\frac{9}{37}+\frac{3i}{74}$$  

• $$\frac{3}{37}+\frac{i}{74}$$  

• $$\frac{21+3i}{100}$$  

• $$\frac{27+6i}{85}$$  

Multiple Choice

Simplify $$\frac{5}{-1-9i}$$  

• $$\frac{-2+18i}{41}$$  

• $$\frac{-5+45i}{82}$$  

• $$\frac{-5+45i}{86}$$  

• $$\frac{-2+9i}{17}$$  

Multiple Choice

Simplify $$\frac{14}{7-6i}$$  

• $$\frac{98+84i}{85}$$  

• $$\frac{35+21i}{34}$$  

• $$\frac{7+7i}{6}$$  

• $$\frac{112+96i}{85}$$  

Multiple Choice

Simplify $$\frac{10-10i}{2+2i}$$  

• $$\frac{30-70i}{29}$$  

• $$5-5i$$  

• $$\frac{1-i}{4}$$  

• $$-5i$$  

Multiple Choice

Simplify   $$\frac{8+5i}{1-7i}$$  

•   $$\frac{-3+76i}{65}$$  

•   $$\frac{11+77i}{50}$$  

•   $$\frac{-11-5i}{7}$$  

• $$\frac{-27+61i}{50}$$  

Multiple Choice

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

• 24
• -48i
• 48i
• 60

Multiple Choice

$$Simplify:\ \ \ \ 2i\left(4\ +\ 3i\right)$$  

• $$-6\ +\ 8i$$  

• $$6\ +\ 8i$$  

• $$-6i\ +\ 8i$$  

• $$-1\ +\ 8i$$  

Multiple Choice

$$\left(5-i\right)^2$$  

• 15-8i

• 36

• 24+10i

• 24-10i

Multiple Choice

Simplify
3i - (4 + 7i)

• -4 + 10i
• 21 - 12i
• 4 - 10i
• -4 - 4i

Multiple Choice

What is the conjugate of -8i?

• -8i

• 8i

• 8

• -8

Multiple Choice

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

• -2+6i
• 12+6i
• -35-16i²
• -35 -16i

Multiple Choice

Simplify: 
(10+ 15i) - (48 - 30i)

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

Multiple Choice

(2i)(3i)

• 5i
• -5
• 6i
• -6

Multiple Choice

Multiply: 
(4 – 3i)(-7 – 2i)

• A.  -23 + 13i
• B.  -23 - 29i
• C.  -34 + 13i
• D.  -34 - 29i

Multiple Choice

Find the product
(1+3i)(2-i)

• 5+5i
• 5-5i
• 2-3i
• 5+7i

Multiple Choice

3+√-4

• 1

• 3-2i

• 5

• 3+2i

Multiple Choice

(-7+6i)²

• 49+36i

• 85

• 13-84i

• 13+84i

Multiple Choice

4+5i+6+6i

• 21i

• 20i+36

• 24+30i

• 10+11i

Multiple Choice

Find the sum.
(5-2i) + (-7+8i)

• -2+6i
• 12+6i
• -35-16i²
• -35 -16i

Multiple Choice

Simplify (11 + 5i)(11 - 5i)

• 121 -110i

• 121 + 110i

• 146

• 121 - 25i²

Poll

How would you rate your understanding of complex numbers?

• 1 (I don't know what a complex number is)

• 2 (I am starting to understand a little bit)

• 3 (Most of it makes sense)

• 4 (I understand it completely)

• 5 (I understand it and could explain it)