Complex numbers Questions and Answers

Find the quotient of the complex numbers. Leave your answer in polar form. Z2 N Z₁ 21 22 * 2₁ = 6 (cos+ i sin ) 22=7 [cos + i sin 5 5 11 11 11 - expression T

Write the number i √-9 in simplest form, without a negative radicand. i√-9 =_________ (Simplify your answer. Type an integer or a fraction.)

Divide: 1 - 5i/ -1 + 6i . Write your answer in a + bi form

Calculate √-4-3i. Give your answer in a + bi form. Give the solution with smallest positive angle. Round to at least one decimal place.

Divide: 6- 6i/ 7 + 2i Write your answer in a + bi form

Rewrite the complex number 8e^1.5i in a + bi form

Rewrite the complex number 5e^6i in a + bi form

Calculate √2+4i. Give your answer in a + bi form. Give the solution with smallest positive angle. Round to at least one decimal place.

Rewrite the complex number 10e^1.5i in a + bi form

Rewrite the complex number 2e^2i in a + bi form

Rewrite the complex number 10e^3i in a + bi form

A group of friends is planning to go to Europe 3 years from now and have agreed to set aside $150 each month for their trip. If they deposit this money at the end of each month into a savings account paying interest at the rate of 6% per year compounded monthly, how much money will be in their travel fund at the end of the third year?

In an orthonrmal cordinate system for thetriangle, a circle inscribed in a triangle with vertices 0 (0.0), P(a.0) and Q(0.a) has a radius of 1. What is the area of this triangle? answer is 3+2√2

Let L. be the line with parametric equations x = -9+31 y=-4-3t z=-7 Find the vector equation for a line that passes through the point P (6, 9, 9) and intersects L at a point that is distance 4 from the point Q-(-9.-4.-7). Note that there are two possible correct answers. Use the square root symbol '√' where needed to give an exact value for your answer.

The area, A, in square feet, of the base of a rectangular storage bin in a warehouse is given by the function A(x) = -2x² + 36x, where x is the width, in feet, of the storage bin. Part A: Which of the following statements would be TRUE? The x-intercepts of the function are 0 and 8, which are a lower bound and an upper bound for the possible values of the length of the storage bin. The x-intercepts of the function are 0 and 8, which are a lower bound and an upper bound for the possible values of the width of the storage bin. The x-intercepts of the function are 0 and 18, which are a lower bound and an upper bound for the possible values of the length of the storage bin. The x-intercepts of the function are 0 and 18, which are a lower bound and an upper bound for the possible values of the width of the storage bin.

The height, h, in feet of the tip of the minute hand of a wall clock as a function of time, t, in minutes can be modeled by the equation h=0.75cos(π/30*(t-15))+8 Which number (from 1 to 12) is the minute hand pointing to at t=0? 3 6 9 12

Solve the equation. 2y + 2(y-8)= 4y -2(y-10) Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution is (Simplify your answer.) B. The solution is all real numbers. C. There is no solution.

Multiply the complex number by its complex conjugate. 4 + 3i

A football team scored 73 points during a game from touchdowns (6pts each), extra points (1pt each), and field goals (3pts each). The coach chastised the kicker afterward for only making half of their extra point attempts. The assistant coach remarked that they made one less field goal than touch downs. How many touchdowns, extra points, and field goals did they make? The team made Number and made Number field goals. touchdowns but only made Number extra point attempts,

A ball is projected directly upward from an initial height of 200 feet with an initial velocity of 64 ft per second. The function s(t) = -16t² + 200t +64 describes the height of the ball in terms of time t. Find the maximum height that the ball reaches. (7 points)

23. Suppose that point p is on a circle with radius r = 15 cm, and ray op is rotating with W = π rad / see. a. Find the distance traveled by P along the circle in time t = 12 sec. b. Find the linear speed v of P.

A rectangle with constant area has possible lengths and widths as shown in the table below. Width vs. Length of a Rectangle Width (w) 2 4 6 8 Which equation can be used to find any corresponding length and width that fit the pattern in this table? 0 1 = Length (/) 37.5 18.75 12.5 9.375 where / is the length, w is the width, and k is a constant (w* 0) O = mw+b, where / is the length, w is the width, and m and b are constants O W: 2, where / is the length, w is the width, and k is a constant /= kw /= aw², where / is the length, w is the width, and a is a constant

The voltage V of an audio speaker can be represented by V-4/P, where P is the power of the speaker. An engineer wants to design a speaker with 484 watts of power. What will the voltage be? volts GITTIS

In this problem, p is in dollars and x is the number of units. The demand function for a certain product is p = 121 - x² and the supply function is p = x² + 6x + 41. Find the equilibrium point. (L (x, p) = Find the consumer's surplus there. (Round your answer to the nearest cent.)

For the equation 6x + 5y = 30, (a) write it in slope-intercept form, (b) give the slope of the line, (c) give the y-intercept, and (d) graph the line. ... (a) The slope-intercept form of the equation is (Simply your answer. Use integers or fractions for any numbers in the equation.) (b) The slope is (Type an integer or a simplified fraction.) (c) The y-intercept is (Type an ordered pair, using integers or fractions.) (d) Use the graphing tool to graph the equation. Click to enlarge graph 10 P 134 224435 10- 75 COME 8 6 -8 10 P M 2201 NOTE A 10

Review the following words and re-write them below the inequality in which they would apply. (Words could be used more than once or not at all.) Union And Or Intersection Compound Inequality |3x1|< 4 12-3x ≥ 5

The conjugate of a complex number a + bi is 25 + 3i. What is a + bi? O-25+ 3i 25-3i

Determine the domain and range of the given quadratic function below. Enter your answer using interval notation. f(x) = 3x² + 12x - 2 (a) Domain: (b) Range:

5 Solve your given pair of complex numbers placing them on an Argand diagram. B = 3 + 2j C = 3 - 2j (a) X+Y (b) Y-X

Identify the conic section represented by the equation by rotating axes to place the conic in standard position. Find an equation of the conic in the rotated coordinates, and find the angle of rotation. Choose one ▾ NOTE: Round your answer to one decimal place if needed. 0 7x² + 10xy + 7y² = 24 =

The price that a farmer receives for radishes is $62.00 per cwt. (100 pounds). The price for processed radishes is $75.00 per cwt and the price for processed radishes at the retail level is $2.15 per pound. The conversion factor for processed radishes is 1.175. What is the farm-to-retail price spread?

5. y 3sin(12(x+π/24)) + 1 5. Write the equation of a sine curve, with smallest possible phase shift, if it has a maximum at (4) and the nearest minimum to the right at (₁-2).

1 Find the indicated values for f(x)=x. a. b. c. a. f(0) = f(0) f(24) f(-24)

To determine the distance between two aircraft, a tracking station continuously determines the distance to each aircraft and the angle A between them (see figure). Determine the distance a between the planes when A= 38°, b = 39 miles, and c = 18 miles. (Round your answer to one decimal place.) a =

Solve the system of first-order linear differential equations.

f(x) is a third-degree polynomial having only real coefficients. It has -1 and -2i as zeros, and the y-intercept(0, -3). Find f(x).

Let : R³Prove thatdefinition!)πR2 be the projection function given by (x, y, z) = (x, y).is a continuous function. (Extra Credit if you use the ε-8

How far away from a lighthouse on shore can a ship be seen if the observer in the lighthouse is 100 ft above the surface of the Earth? Radius of the Earth is 20.93 x 10^6 feet 1000 FT 5000 FT 22032 FT 10297 FT

Geometry Determine each of the following for the function y= 6 cos(5(x +45)) – 3. Justify your answer. i.The amplitude ii.The period Formula: 2TT/K=360/K (calculate exact number) iii.The phase shift iv.The vertical shift of the function b. Sketch the one cycle of the function in part (a) on grid paper without using a table of values. Explain your reasoning.