Lesson 5: Complex and Imaginary Numbers

Complex and Imaginary Numbers

Adding or Subtracting complex numbers

Add or subtract "LIKE" terms (imaginary can only combine with imaginary terms, and real terms can only combine with real terms)

What is an imaginary number?

Multiple Choice

Find the difference.
(6 - 8i) - (1 - 3i)

• 9 + 5i
• 5 - 11i
• 5 - 5i
• 7 + 5i

Multiple Choice

Rationalize the denominator and simplify completely.

• $$\frac{-3-i}{4}$$

• $$\frac{3+i}{4}$$

• $$\frac{-3+i}{4}$$

• $$\frac{3-i}{4}$$

Multiple Choice

$$\sqrt{-80}$$  

• $$2i\sqrt{20}$$  

• $$4i\sqrt{5}$$  

• $$-8\sqrt{10}$$  

Multiple Choice

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

• -2+6i
• 12+6i
• -35-16i²
• -35 -16i

Multiple Choice

$$3\sqrt{-90}$$  

• $$3i\sqrt{10}$$  

• $$9i\sqrt{10}$$  

• $$27i\sqrt{10}$$  

Multiple Choice

Simplify
3i - (4 + 7i)

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

Multiple Choice

Simplify
2i - 7i + 10

• -5i+10
• 5i
• 9i+10
• 5i+10

Multiple Choice

Subtract: (9 - 2i) - (-2 + 5i)

• 7 - 7i
• 11 - 7i
• 11 + 3i
• 7 + 3i

Multiple Choice

Add: (3 - 6i) + (-2 - 2i)

• 5+8i
• 1+8i
• 1-8i
• -18-6i

Multiplication

• Multiply using the box method or FOIL

• Simplify using facts about i

Multiple Choice

Multiply: 
(4 – 3i)(7 + 2i)

• A.  22 - 13i
• B.  28 - 19i
• C.  34 - 13i
• D.  -34 - 29i

Multiple Choice

Multiply: (2 + 4i)( -3 - 5i)

• 14 - 22i
• -26 - 22i
• 14 + 2i
• 26 + 22i

Multiple Choice

Multiply:
(2-5i)(2+5i)

• 29
• 4 - 25i
• 25 - 10i
• -21

​Rationalizing Complex Denominators

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Multiple Choice

What is the conjugate of -2+5i?

• -5+2i
• -2-5i
• 2+5i
• 5-2i

Multiple Choice