Introduction to Imaginary Numbers

Imaginary Numbers (Complex Numbers)

Open Ended

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What is a Complex Number?

• Looks like this 4 + 2i

• The 4 is a Real Number and the 2i is an Imaginary Number

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

• ​Simplified negative radicals

• ​Add/Sub complex numbers

• ​Multiplied complex numbers

• ​Rationalized complex denominators

​Things we have learned

Multiplying Complex Numbers

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

Poll

Pick the GOAT

​Rationalizing Complex Denominators

​

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

What is the conjugate of -2+5i?

• -5+2i
• -2-5i
• 2+5i
• 5-2i

Multiple Choice