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

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

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

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

• 5 - 2i

• -5 - 2i

• 5 + 2i

• -5 + 2i

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

What is i to the power of 4?

• i

• 1

• -1

• 0

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

• -1

• 1

• -i

• i

Which of the following is true about i cubed?

• It equals i

• It equals -i

• It equals 1

• It equals -1

What is the result of i squared times i?

• -i

• 1

• -1

• i