Solving Equations and Complex Numbers

The video tutorial demonstrates solving a quadratic equation involving complex numbers. It begins by setting up the equation and isolating the squared term. The square root property is applied to simplify the equation, followed by rationalizing the expression. The solution is then presented in standard form, highlighting the complex solutions obtained.

What is the initial equation given in the problem?

• 2(3x - 1)^2 + 9 = 0

• 3x^2 - 1 + 9 = 0

• 3(2x - 1)^2 + 9 = 0

• 2x^2 - 3x + 9 = 0

What is the first step to isolate the squared term?

• Subtract 9 from both sides

• Divide both sides by 3

• Add 9 to both sides

• Multiply both sides by 2

After isolating the squared term, what is the equation?

• (3x - 1)^2 = -9/2

• (3x - 1)^2 = 9/2

• (3x - 1)^2 = 9

• (3x - 1)^2 = -9

What property is applied to solve the equation after isolating the squared term?

• Factoring

• Completing the Square

• Square Root Property

• Quadratic Formula

What is the simplified form of the square root of negative nine?

• -3

• -3i

• 3i

• 3

What is the imaginary unit 'i' equivalent to?

• √-1

• √1

• -1

• 1

How is the expression 3i over the square root of 2 rationalized?

• Multiply by 2

• Multiply by square root of 2

• Multiply by square root of 3

• Multiply by 3

What is the next step after rationalizing the expression?

• Divide by 3

• Multiply by 3

• Subtract 1 from both sides

• Add 1 to both sides

What is the result of multiplying the numerator and denominator by the square root of 2?

• 3√2/2

• 3i/2

• 3i√2/2

• 3/2

What is the value of the square root of 4?

• 1

• 2

• 3

• 4