Understanding Complex Numbers and Operations

Amal Kumar explains how to remove 'i' from the denominator of a complex number expression by rationalizing it. The process involves multiplying and dividing by the conjugate, simplifying the expression, and writing it in standard form. The tutorial covers the multiplication of complex numbers, simplification using the properties of 'i', and the final expression in standard form.

What is the main goal when removing 'i' from the denominator of a complex number?

• To make the expression more complex

• To increase the imaginary part

• To express the number in standard form

• To eliminate the real part

What is the standard form of a complex number?

• a / bi

• a + bi

• a - bi

• a * bi

Why do we need to rationalize a complex number?

• To eliminate the imaginary unit from the denominator

• To express it in polar form

• To remove the real part

• To make calculations easier

What is the conjugate of a complex number 2 - 3i?

• 2 + 3i

• 2 - 3i

• -2 + 3i

• -2 - 3i

How do you rationalize a complex number?

• Add the conjugate

• Multiply and divide by the conjugate

• Divide by the imaginary part

• Multiply by the real part

What is the result of multiplying a complex number by its conjugate?

• A real number

• An imaginary number

• A complex number

• Zero

What is the value of i squared?

• 1

• -1

• 0

• i

What is the result of 3i squared?

• 9

• -9

• -3i

• 3i

What is the simplified form of 4 - 9?

• 13

• -5

• 5

• -13

What is the final expression of the complex number in standard form?

• -5/13 + 12/13i

• 5/13 - 12/13i

• 12/13 - 5/13i

• -12/13 + 5/13i