Exploring Complex Zeros in Polynomials

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

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

• i

• 0

• -1

• 1

Which of the following represents a complex number?

• a / b

• a + bi

• a * b

• a - b

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

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

• 11 + 2i

• 11 - 2i

• -5 + 10i

• -5 - 10i

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

• 5

• ±5i

• -5

• 5i

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

• Completing the square

• Substitution

• Synthetic division

• Graphing

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

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

How many zeros should a polynomial of degree 5 have?

• 7

• 1

• 3

• 5