Complex Numbers and Their Operations

The video tutorial explains how to cube a complex number by multiplying it with itself three times. The process involves multiplying two complex numbers at a time, similar to multiplying binomials, and simplifying the result using the property that i squared equals negative one. The tutorial walks through the steps of distributing terms, combining like terms, and simplifying to reach the final result of cubing the complex number three minus two i, which equals negative nine minus 46i.

What is the first step in cubing a complex number?

• Use a shortcut formula

• Write out the complex number three times

• Divide the complex number by three

• Add the complex number to itself

How do you multiply two complex numbers?

• By adding their real parts

• By subtracting their imaginary parts

• By using repeated distribution

• By dividing their coefficients

What is the result of multiplying 3 by -2i?

• -6i

• 6i

• -3i

• 3i

What is the value of i squared?

• 1

• -1

• 0

• i

What is the simplified form of 4i squared?

• 4

• -4

• 8

• 0

What is the result of combining 9 and -4?

• -13

• 13

• -5

• 5

What is the result of multiplying 5 by 3?

• 5

• 8

• 15

• 10

What is the result of multiplying -12i by -2i?

• 24i

• -24i

• 24

• -24

What is the final real part of the cube of 3 - 2i?

• -46

• 9

• -9

• 46

What is the final imaginary part of the cube of 3 - 2i?

• -46i

• 46i

• -9i

• 9i