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What complex number lies below the real axis and to the right of the imaginary axis?
Wiki User
∙ 11y ago
Complex numbers whose polar representation is (r, theta) where 3*pi/2 < theta < 2*pi.
Wiki User
∙ 8y ago
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How do you solve the power of an imaginary number?
It helps to think about imaginary and complex numbers graphically. Euler's Formula (see related link): eiΘ = cos(Θ) + i sin(Θ) {Θ is in radians}. Note that both eiΘ and [cos(Θ) + i sin(Θ)] have a magnitude of 1, so multiply by the magnitude: AeiΘ = Acos(Θ) + Ai sin(Θ). You now have a graphical representation of complex numbers, with real numbers on the horizontal axis, pure imaginaries on the vertical axis, and all other complex numbers placed on the 'complex plane'. The angle is a direction, from the origin, and the magnitude A tells how far away from the origin that the position is. With pure imaginary numbers you can have Θ = pi/2 radians (90°, vertical), and let A be either positive or negative (up or down). From the rules for exponents and powers, you now have the imaginary number z = ei*pi/2, and (ex)n = ex*n, so zn = (ei*pi/2)n = ei*n*pi/2 , so switching to degrees for simplicity: n Θ 0 0° (Points to the right: positive real) 1 90° (Pointing straight up: imaginary positive number) 2 180° (Points to the left: real negative number) 3 270° (Points straight down: imaginary negative) 4 360° (Points to the right: real positive ), same as 0° Note it goes in a circle and repeats. Odd integer values of n will be pure imaginary and even integers will be real numbers. Non-integers will put the angle so it is a complex number. Negative exponents cause it to move in a clockwise direction on the circle, rather than counterclockwise (for positive exponents). Now that you know the direction, you only need to take An, as a power, and then point it in the proper direction. So if the power of A yields a positive number, the answer will be in the direction, but if it yields a negative number (odd integer powers of a negative A), then it's in the opposite direction (add 180° to the angle).
How do you plot 6-i on a complex plane?
You go 6 in positive x-direction ("right") and one in negative y-direction ("down"), there is your complex number, drwa an arrow reaching from the center to this point.
Is there a complex number that is equal to the square of its conjugate?
If the number is (a + bi) then the conjugate is (a - bi)so set (a + bi) = (a - bi)² = a² - 2abi - b².This can be split into to separate equations, because the real part on the left must equal the real part on the right, and the imaginary part on the left must equal the imaginary on the right.a = a² - b² ; and b = -2ab.Use the 2nd equation to solve for a, by dividing both sides by b: 1 = -2a ---> a = -1/2.Plug this into the first equation, and solve for b: -1/2 = (-1/2)² - b² --- b² = 3/4.So b = (±√3)/2, So the number -1/2 + i(√3)/2, and its conjugate -1/2 - i(√3)/2, will solve the conditions.
What is veyselic numbers?
Veyselic numbers are Arabic numbers written from right to left. Most significant digits are on the right. For example number ten is .l (See related link below for more information.)
Evaluate and express this complex number in standard form the absulote value of 5-12i?
The absolute value of a complex number is it's magnitude (distance from the origin). Think about complex numbers graphically, with reals on the horizontal axis, and imaginaries on the vertical axis. Now you have a right triangle: From the origin move to the right 5 units, then move down 12 units. The absolute value, or magnitude, is the length of the hypotenuse. For this triangle, it is 13: sqrt(5^2 + 12^2) = sqrt(25+144) = sqrt(169) = 13. For magnitudes, we are only interested in the positive square root.
What are examples of complex numbers?
z=x+iy, where x and y are real numbers. Complex numbers can produce interesting graphs. If you graphed the above, you would get vertical and horizontal lines. But what happens when you graph 1/z ? When you work it out, you get two equations which are at right angles to each other. You get u=x/(xx+yy) and v=-y/(xx+yy) which are families of concentric circles at right angles to each other.3i. Combining the real number 3 with the imaginary number i creates a complex number.
Is -4 a imaginary number?
No, both positive and negative numbers are part of the so-called "real" numbers. The so-called "imaginary" numbers are outside the number line.Imagine the real numbers as a line from left to right, and the imaginary numbers a a separate line, from top to bottom. The place where they meet is zero. Positive is to the right of zero, negative to the left, imaginary numbers like +i or +3i to the top of zero, and negative imaginary numbes like -5i to the bottom of zero.
What does the imaginary number equal in math?
The following may seem far-fetched if you are not accustomed to imaginary or complex numbers, so before I continue, let me assure you that complex numbers have many practical applications, including electricity, quantum mechanics, art, and several other more.The imaginary number is neither a positive nor a negative number. Imagine two perpendicular axes of numbers. The directions are arbitrary, but the way it is commonly drawn, from left to right you have the real numbers - the numbers you are probably most familiar with, which include positive and negative numbers. Positive at the right, negative at the left. The number line which you may have seen already.From top to bottom is another line, that crosses the origin - the line of the imaginary numbers. One unit up is +i, two units up is +2i, one unit down (from the origin, or zero) is -i, two units down is -2i, etc. The "imaginary unit", then, is called "i", although in electricity the letter "j" is used instead (to avoid confusion with the unit for current).A combination of a real number and an imaginary number is called a complex number - for example, 2 + 3i. Adding and subtracting complex numbers is fairly straightforward. Just add the corresponding terms. To multiply complex numbers, multiply them as you normally multiply binomials - then use the definition i2 = -1.It so happens that when complex numbers are used, not only do negative numbers have a square root, but any root - square root or otherwise - has a solution. In a way, this makes the complex numbers more "complete" than the real numbers.Of course, common sense should be used. Just as negative or fractional numbers don't make sense for some real-life problems, complex numbers don't make sense for some real-life problems, either. So if, for example, the quadratic formula gives you a complex solution (or a negative solution, for that matter), analyze the original problem to see whether the specific solutions found make sense, given the problem statement.
How do you find the absolute value of a complex number?
-- square the size of the real part -- square the size of the imaginary part -- add the two squares together -- take the square root of the sum. Hey! That sounds a lot like the Pythagoras thing in a right triangle.
How do you solve the power of an imaginary number?
It helps to think about imaginary and complex numbers graphically. Euler's Formula (see related link): eiΘ = cos(Θ) + i sin(Θ) {Θ is in radians}. Note that both eiΘ and [cos(Θ) + i sin(Θ)] have a magnitude of 1, so multiply by the magnitude: AeiΘ = Acos(Θ) + Ai sin(Θ). You now have a graphical representation of complex numbers, with real numbers on the horizontal axis, pure imaginaries on the vertical axis, and all other complex numbers placed on the 'complex plane'. The angle is a direction, from the origin, and the magnitude A tells how far away from the origin that the position is. With pure imaginary numbers you can have Θ = pi/2 radians (90°, vertical), and let A be either positive or negative (up or down). From the rules for exponents and powers, you now have the imaginary number z = ei*pi/2, and (ex)n = ex*n, so zn = (ei*pi/2)n = ei*n*pi/2 , so switching to degrees for simplicity: n Θ 0 0° (Points to the right: positive real) 1 90° (Pointing straight up: imaginary positive number) 2 180° (Points to the left: real negative number) 3 270° (Points straight down: imaginary negative) 4 360° (Points to the right: real positive ), same as 0° Note it goes in a circle and repeats. Odd integer values of n will be pure imaginary and even integers will be real numbers. Non-integers will put the angle so it is a complex number. Negative exponents cause it to move in a clockwise direction on the circle, rather than counterclockwise (for positive exponents). Now that you know the direction, you only need to take An, as a power, and then point it in the proper direction. So if the power of A yields a positive number, the answer will be in the direction, but if it yields a negative number (odd integer powers of a negative A), then it's in the opposite direction (add 180° to the angle).
Is London below the equator?
No sir it is not. The equator is the imaginary line that goes horizontally (left to right) around the Earth. London is a city in Europe, all of Europe is above the equator.
What is Imaginary lines at right angles to a surface?
jnjhnh
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