Complex Numbers and Their Operations

The video tutorial covers various mathematical concepts involving complex numbers and algebraic expressions. It begins with calculating the absolute value of complex numbers, followed by simplifying expressions using distribution and the FOIL method. The tutorial also explores expanding complex numbers, calculating powers of the imaginary unit i, and simplifying square roots. Additionally, it demonstrates rationalizing denominators and finding the absolute value of complex expressions. The tutorial concludes with solving equations to find x and y values.

What is the absolute value of the complex number 6 + 8i?

• 14

• 8

• 10

• 12

After distributing and combining like terms, what is the simplified form of 5(2 - 3i) - 4(4 + 6i)?

• 6 - 39i

• -6 + 39i

• 6 + 39i

• -6 - 39i

What is the result of expanding (3 + 7i)^2?

• 40 - 42i

• -40 - 42i

• 40 + 42i

• -40 + 42i

What is the value of i raised to the 59th power?

• 1

• -1

• i

• -i

What is the simplified form of the expression involving the square root of negative fourteen?

• Positive root six

• Negative root six

• Positive root seven

• Negative root seven

What is the result of rationalizing the denominator of 9/(3 + root 2i)?

• 27/11 - 9 root 2/11 i

• 27/11 + 9 root 2/11 i

• 9/11 - 27 root 2/11 i

• 9/11 + 27 root 2/11 i

What is the absolute value of the expression 5i^12 - 3i^19?

• Square root of 41

• Square root of 50

• Square root of 34

• Square root of 25

What is the simplified form of the expression (3 + 2i)(4 + 3i)?

• 6/25 + 17/25i

• 12/25 + 17/25i

• 6/25 - 17/25i

• 12/25 - 17/25i

What is the simplified form of the expression 4 + 3i and 3 + 2i?

• 6/25 + 17/25i

• 12/25 + 17/25i

• 12/25 - 17/25i

• 6/25 - 17/25i

How do you find the value of x + y if x = 3 and y = -2?

• 1

• -1

• 0

• 2