Real numbers - practice problems - page 4 of 9
Direction: Solve each problem carefully and show your solution in each item.Number of problems found: 161
- Complex plane mapping
Show that the mapping w = z +c/z, where z = x+iy, w = u+iv, and c is a real number, maps the circle |z| = 1 in the z-plane into an ellipse in the (u, v) plane. - Infinitely 3818
We have 2 numbers. If we multiplied the first number's third root by the second number's square root, we would get the number 18. Determine these 2 numbers. Calculate only the integer solution if the problem has infinitely many solutions in the set of rea - Cotangent
If the angle α is acute, and cotan α = 1/3. Determine the value of sin α, cos α, and tan α. - Real and imaginary parts
Let z1=x1+y1i and z2=x2+y2i Find: a = Im (z1z2) b = Re (z1/z2) - Root
Use the law of square roots: cbrt (sqrt[2] (sqrt[4] (6))) = sqrt[n] (6) - Evaluate complex expr
Evaluate the expression (-4-7i)-(-6-9i) and write the result in the form a+bi (Real + i* Imaginary). - Imaginary numbers
Find two imaginary numbers whose sum is a real number. How are the two imaginary numbers related? What is their sum? - Quarter circular
The wire hooked around the perimeter of the quarter-circular arc has a length of 14π+56. Determine the radius of the circle arc. - Is complex
Are these numbers 2i, 4i, 2i + 1, 8i, 2i + 3, 4 + 7i, 8i, 8i + 4, 5i, 6i, 3i complex? - Deposit and saving
How long will the deposit of € 2,000 increase at an interest rate of 4.6% p. a. at 2500 €? (Ideally, calculate without logarithms) - Domains of functions
F(x)=x²-7x and g(x)=5-x² The domain of (fg)(x) is. ... The domain of (f/g)(x). .. - Quadratic equation
Determine the numbers b and c that the numbers x1 = -8 and x2 = -1 were roots of the quadratic equation: -3x ² + b x + c = 0 - Real roots
Determine the real root of the equation: x-3: x-8 = 32 - Equation
Equation f(x) = 0 has roots x1 = 25, x2 = 64, x3 = 9. How many roots have equation f(x²) = 0? - Biquadratic
By introducing a new variable, solve the biquadratic equation: - x 4 +277 x² -15876=0 - Specific series
Complete the next three members of the series formed according to a specific rule: 1, √2, 9, 2, 25,. ..,. ..,. .. - Factors
Can the expression 4x ² -47.6x +39.6 be factored into rational factors? - The sum 15
The sum of the real numbers x and y is 24. Their difference is 12. What is the value of xy? - Coordinate
Determine the unknown coordinate of the point M [x, 54] of the graph of the function f by rule: y = 3x - What is 21
What is the next number? What is the 7th number? 160, 80, 40, 20, 10, _
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