Complex Numbers and Their Operations

The video tutorial covers operations with complex numbers, including simplifying expressions, multiplying and dividing complex numbers, and calculating powers of the imaginary unit i. It explains the use of the FOIL method for multiplication and the conjugate for division, and provides step-by-step solutions to example problems.

What is the result of combining 8 + 5i and 7i?

• 13 + 7i

• 8 + 12i

• 15 + 10i

• 13 + 12i

Tags

CCSS.HSN.CN.A.1

How does i squared simplify?

• 0

• -1

• 1

• i

What is the product of (3 + 4i) and (5 - 2i)?

• 15 + 8i

• 23 + 14i

• 23 - 14i

• 15 - 8i

Tags

CCSS.HSN.CN.A.2

When multiplying complex numbers, what does the term 'FOIL' stand for?

• First, Outer, Inner, Last

• First, Outer, Inverse, Last

• First, Only, Inner, Last

• First, Outer, Inner, Least

Tags

CCSS.HSN.CN.A.3

What is the conjugate of the complex number 5 + 2i?

• 5 - 2i

• -5 - 2i

• 5 + 2i

• -5 + 2i

Tags

CCSS.HSN.CN.A.3

How do you simplify the expression (2 + 3i) / (5 + 2i)?

• Multiply by the conjugate of the numerator

• Multiply by the conjugate of the denominator

• Divide by the conjugate of the numerator

• Divide by the conjugate of the denominator

Tags

CCSS.HSN.CN.A.2

What is i to the power of 4?

• i

• 1

• -1

• 0

Tags

CCSS.HSN.CN.A.2

What is the value of i raised to the 283rd power?

• -1

• 1

• -i

• i

Tags

CCSS.HSN.CN.A.2

Which of the following is true about i cubed?

• It equals i

• It equals -i

• It equals 1

• It equals -1

Tags

CCSS.HSN.CN.A.2

What is the result of i squared times i?

• -i

• 1

• -1

• i

Tags

CCSS.HSN.CN.A.2