Front

What is the value of i^4?

Back

1

Front

Solve the equation x^2 = -121 over the complex numbers.

Back

x = \pm 11i

Front

What is the maximum height of a projectile modeled by the equation y = -16x^2 + 32x + 20?

Back

36 ft

Front

Simplify: -6i + 3i

Back

-3i

Front

Solve the equation x^2 + 7x = 18.

Back

x = -9, x = 2

Front

What is the definition of a complex number?

Back

A complex number is a number that can be expressed in the form a + bi, where a and b are real numbers and i is the imaginary unit.

Front

What is the imaginary unit i?

Back

The imaginary unit i is defined as the square root of -1, i.e., i = \sqrt{-1}.

Front

What is the quadratic formula?

Back

The quadratic formula is given by x = \frac{{-b \pm \sqrt{{b^2 - 4ac}}}}{{2a}} for a quadratic equation ax^2 + bx + c = 0.

Front

What does it mean for a quadratic equation to have complex solutions?

Back

A quadratic equation has complex solutions when the discriminant (b^2 - 4ac) is negative, indicating that the roots are not real numbers.

Front

How do you find the vertex of a parabola given by the equation y = ax^2 + bx + c?

Back

The vertex can be found using the formula x = -\frac{b}{2a}.