Why is cis notation beneficial when working with complex numbers in polar form?

Evaluate (3 cis 120°)^4 using DeMoivre's Theorem and compare it to multiplying the complex number by itself four times.

Out of two solutions of the given nonlinear system, one solution is (0, _):

When converting the system of equations 2x + 3y = 5 and x - y = 2 into a matrix, why is it important to align the variables consistently?

Which of the following best describes Cramer's Rule?

Graph the following system of inequalities, and evaluate the objective function at each corner of the graphed region. Then, identify the values of x and y for which the maximum value is found.

How does the angle of the slicing plane affect the formation of a parabola?

What is the center and radius of the circle given by the equation (x - 1)² + (y + 2)² = 9?

What is the geometric definition of an ellipse?

By completing the square, write the given equation into the standard form, and then identify the vertex, focus, and directrix of the parabola. Also, graph the parabola in a rectangular coordinate system.
x² + 10x - 12y + 13 = 0

For the hyperbola (x^2/49) - (y^2/25) = 1, calculate the coordinates of the vertices.

For the hyperbola (y-2)^2/36 - (x+1)^2/16 = 1, what are the coordinates of the vertices?

What is the formula for the sequence 1/2, 2/3, 3/4, 4/5?

If the sequence is 10, 15, 20, 25, what is the common difference?

The first term (a₁) and the common ratio (r) of a geometric sequence are given. Find the specified term using the general term (n^th term) formula.

Find a₁₅ when a₁ = 4, r = -3.

Simplify the expression 8! / 6!.

Find the difference quotient, [f(x + h) - f(x)]/h, of the function: f(x) = x⁵ - 2

What is the theoretical probability of rolling a 2 on a standard 6-sided die?

Using a table of values, find the limit of f(x) = 1/x as x approaches 0 from the right.

Under what condition can direct substitution be used to find the limit of a rational function?

Evaluate the continuity of the piecewise function f(x) = {3x + 1 for x < 0, x^2 for x ≥ 0} at x = 0.

Which of the following statements is true about a tangent line?

A population of bacteria, P(t), is modeled by the function P(t) = 500/(1 + 0.05t). What is the population as time t approaches infinity?

If q_n = 4/(n^2 + 1), what is the limit as n approaches infinity?

Calculate the area under the curve of f(x) = 2x + 1 from x = -1 to x = 2 by dividing the area into a rectangle and a triangle.