How to rewrite an expression in the standard form of a complex number using i

The video tutorial explains how to simplify expressions using the imaginary unit 'i'. It begins by introducing the concept of 'i' and its necessity for handling square roots of negative numbers. The instructor demonstrates rewriting expressions with 'i' and applying rules of exponents. The process of simplifying square roots is detailed, including attempts to find the largest square number that divides evenly into a given number. The tutorial concludes with the realization that some expressions cannot be further simplified.

Why is the imaginary unit 'i' used in simplifying expressions?

• To solve linear equations

• To represent the square root of a negative number

• To simplify fractions

• To convert decimals to fractions

What does the imaginary unit 'i' represent?

• The square root of 1

• The square root of -1

• The square root of 0

• The square root of 2

How is the expression sqrt(-42) rewritten using 'i'?

• 42 * sqrt(2) * i

• 42 * sqrt(2) * sqrt(-1)

• 42 * sqrt(-1) * i

• 42 * sqrt(-1)

Which of the following is the largest square number that divides 42?

• 16

• 9

• 4

• None of these

What conclusion is reached about simplifying sqrt(42)?

• It cannot be simplified further

• It can be simplified to sqrt(14)

• It can be simplified to sqrt(7)

• It can be simplified to sqrt(21)