The video tutorial introduces imaginary numbers, explaining their historical context and necessity in solving equations with negative square roots. It then explores complex numbers, detailing their structure and basic operations. The tutorial demonstrates how complex numbers are used to solve polynomial equations, including synthetic division and finding zeros. Finally, it provides practice problems to reinforce the concepts discussed.

What is the imaginary unit 'i' defined as?

• The square root of 0

• The square root of 1

• The cube root of -1

• The square root of -1

Tags

CCSS.HSN.CN.A.1

If the square root of -1 is 'i', what is i squared?

• i

• 0

• -1

• 1

Tags

CCSS.HSN.CN.A.1

Which of the following represents a complex number?

• a / b

• a + bi

• a * b

• a - b

Tags

CCSS.HSN.CN.A.1

How do you add two complex numbers?

• Add the real parts and add the imaginary parts

• Multiply the real parts and add the imaginary parts

• Subtract the real parts and add the imaginary parts

• Add the real parts and subtract the imaginary parts

Tags

CCSS.HSN.CN.A.2

What is the result of multiplying (3 + 4i) and (1 - 2i)?

• 11 + 2i

• 11 - 2i

• -5 + 10i

• -5 - 10i

Tags

CCSS.HSN.CN.A.2

What is the solution to the equation x^2 + 25 = 0?

• 5

• ±5i

• -5

• 5i

Tags

CCSS.HSA-REI.B.4B

CCSS.HSN.CN.C.7

When solving a quadratic equation that doesn't factor, which method can be used?

• Completing the square

• Substitution

• Synthetic division

• Graphing

Tags

CCSS.HSA-REI.B.4B

What must be done if a term is missing in synthetic division?

• Ignore the term

• Add a zero for the missing term

• Add one for the missing term

• Subtract one for the missing term

Tags

CCSS.HSA.APR.D.6

What is the fundamental theorem of algebra related to complex numbers?

• The degree of a polynomial is equal to the number of real roots

• The degree of a polynomial is equal to the number of complex roots

• The degree of a polynomial is equal to the number of zeros

• The degree of a polynomial is equal to the number of imaginary roots

Tags

CCSS.HSN.CN.C.9

How many zeros should a polynomial of degree 5 have?

• 7

• 1

• 3

• 5