Rationalizing Complex Number Denominators

The video tutorial by Amal Kumar explains the process of rationalizing the denominator of complex numbers using the conjugate method. It begins with an introduction to the technique, followed by a step-by-step application of multiplying and dividing by the conjugate. The tutorial simplifies the expression using the property i^2 = -1 and concludes by rearranging the expression into the standard a + bi form, ensuring no complex number remains in the denominator.

What is the primary goal of rationalizing the denominator in complex numbers?

• To make the numerator a real number

• To eliminate the complex number from the denominator

• To simplify the expression to a single number

• To convert the expression into a fraction

What technique is used to rationalize the denominator of complex numbers?

• Division

• Expansion

• Factorization

• Conjugation

What is the conjugate of the complex number 1 - 2i?

• 1 + 2i

• 1 - 2i

• -1 + 2i

• -1 - 2i

In the example given, what is the initial expression before rationalization?

• 1 over 3i - 2i

• 3i over 1 - 2i

• 1 over 3i + 2i

• 3i over 1 + 2i

When multiplying by the conjugate, what happens to the denominator?

• It becomes zero

• It remains unchanged

• It becomes a complex number

• It becomes a real number

What is the result of multiplying 3i by 1 + 2i?

• 3i + 6i^2

• 3i + 6i

• 3 + 6i

• 3 - 6i

What is the value of i squared in complex numbers?

• i

• 0

• -1

• 1

What happens to the imaginary part of the denominator after rationalization?

• It becomes negative

• It remains the same

• It doubles

• It becomes zero

How is the expression 3i - 6 divided by 5 rearranged into standard form?

• 6/5 - 3/5i

• 3/5 - 6/5i

• -6/5 + 3/5i

• -3/5 + 6/5i

After simplification, what is the real part of the expression?

• -3/5

• -6/5

• 6/5

• 3/5