Algebra 2 - Simplifying a complex number by multiplying by i on the top and bottom, 5/i

The video tutorial explains the concept of imaginary numbers, particularly focusing on the imaginary unit 'i'. It discusses why division involving 'i' in the denominator is not straightforward and introduces the method of multiplying by the conjugate to simplify such expressions. The tutorial further explains how multiplying by the same number in the numerator and denominator creates an equivalent fraction, using examples to illustrate the simplification process. The session concludes with a simplified expression, demonstrating the effectiveness of these techniques.

What is the imaginary unit 'i' defined as?

• The square root of -1

• The square root of 1

• The square root of 0

• The square root of 2

Why is it not intuitive to divide a real number by an imaginary number?

• Because imaginary numbers cannot be divided by real numbers

• Because it doesn't make sense to divide a real quantity by an imaginary one

• Because imaginary numbers are larger than real numbers

• Because imaginary numbers are not numbers

What is the purpose of multiplying by the conjugate when simplifying expressions with imaginary numbers?

• To convert the expression into a real number

• To eliminate the imaginary unit from the denominator

• To make the expression more complex

• To increase the value of the expression

What happens when you multiply 'i' by itself?

• It becomes 0

• It becomes 2

• It becomes -1

• It becomes 1

In the example provided, what is the simplified form of 5i over i squared?

• 5

• -5

• 5i

• -5i