Algebra 2 Learn how to multiply by conjugate to rationalize the denominator complex numbers, i/(3-i)

The video tutorial addresses a common mistake students make when multiplying by i in binomials. It explains why simply multiplying by i is incorrect and introduces the concept of using the conjugate to simplify expressions. The tutorial demonstrates the application of the distributive property and how to rewrite expressions in standard form, emphasizing the importance of dividing terms correctly.

What is a common mistake students make when multiplying complex numbers?

• They use the box method incorrectly.

• They forget to multiply by the conjugate.

• They only multiply by 'i' once.

• They multiply by both terms of the binomial.

Why is it important to multiply by the conjugate of a binomial?

• It results in a difference of squares, canceling out middle terms.

• It simplifies the expression to a single term.

• It increases the value of the expression.

• It changes the sign of the imaginary part.

What happens to the middle terms when multiplying two binomials using the conjugate?

• They remain unchanged.

• They double in value.

• They become imaginary numbers.

• They cancel each other out.

How should the expression be rewritten in standard form?

• By adding the real and imaginary parts.

• By dividing each term by the denominator.

• By multiplying the numerator by the denominator.

• By subtracting the imaginary part from the real part.

What is the final step in simplifying the expression?

• Multiplying by the conjugate again.

• Dividing each term by the denominator.

• Subtracting the real part from the imaginary part.

• Adding the real and imaginary parts.