Algebra 2 - Learn how to divide an imaginary number by a complex number by rationalizing denominator

The video tutorial addresses a common mistake students make when dealing with the imaginary unit 'I' in the denominator of a fraction. It explains why multiplying by I/I is not effective when a binomial is present in the denominator, as it leads to an unwanted imaginary component. Instead, the tutorial introduces the concept of multiplying by the conjugate to eliminate the imaginary unit from the denominator. The process involves using the difference of squares and simplifying the expression to achieve a standard form solution. The final answer is presented in the form A+BI, ensuring clarity and correctness.

What is a common mistake students make when they see 'i' in the denominator?

• They divide the numerator by i.

• They add i to both the numerator and denominator.

• They subtract i from the numerator.

• They multiply by i/i without considering the binomial.

Why is multiplying by the conjugate effective in simplifying expressions with 'i' in the denominator?

• It eliminates the imaginary part completely.

• It uses the sum of two squares.

• It applies the difference of two squares.

• It doubles the value of the expression.

What is the result of multiplying a binomial by its conjugate?

• The difference of two squares.

• A single imaginary number.

• A complex number with no real part.

• The sum of two squares.

How do you rewrite the expression in standard form after simplifying?

• By dividing each term by the denominator.

• By multiplying the numerator by the denominator.

• By subtracting the imaginary part from the real part.

• By adding the real and imaginary parts.

What is the standard form of a complex number?

• A * BI

• BI + A

• A + BI

• A - BI