Q: Find the complex number that is farthest away from the complex plane?

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If you are given a plane, you can always find and number of points that are not in that plane but, given anythree points there is always at least one plane that goes through all three.

The number 1 is its own square root, cube root, etc. in the real number system. To find complex roots of unity, we use the unit circle from trigonometry, coupled with the complex plane, where the x-axis is the real axis, and the y-axis is the imaginary axis. In that coordinate system, the number 1 corresponds to the point (1, 0) and the complex number 1 + 0i. Every complex number a + bi corresponds to the point (a, b) in the complex plane. To find roots of 1, we divide the unit circle up into as many sectors as the number of roots we are trying to find. For cube roots, that's 3 of course, so we divide the unit circle up into 3 sectors of 120 degrees (or 2pi/3 radians) each. So the three cube roots we want are located at the points 120 degrees around the unit circle from (1, 0). Since points on the unit circle have coordinates (cos(theta), sin(theta)), the first one we come to will be (cos(120), sin(120)) = (-1/2, Sqrt(3)/2). This point corresponds to the complex number -1/2 + (sqrt(3)/2)*i. The next point on the circle, 120 degrees from the last one, is (cos(240), sin(240)) = (-1/2, - sqrt(3)/2) = -1/2 - (sqrt(3)/2)*i. Now you have the three cube roots of unity: 1, -1/2 + (sqrt(3)/2)*i, and -1/2 - (sqrt(3)/2)*i. There's much more to all this, involving something called DeMoivre's Formula or Theorem.

another point

yes, you can find a real root to the cube root of any negative real number. There will also be two complex roots which satisfy it, as well.

The square of a "normal" number is not negative. Consequently, within real numbers, the square root of a negative number cannot exist. However, they do exist within complex numbers (which include real numbers)and, if you do study the theory of complex numbers you wil find that all the familiar properties are true.

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The answer depends on what group or field the function is defined on. In the complex plane, the range is the complex plane. If the domain is all real numbers and the radical is an odd root (cube root, fifth root etc), the range is the real numbers. Otherwise, it is the complex plane. If the domain is non-negative real numbers, the range is also the real numbers.

To find out information on the 904 plane, one must contact the airport it has flown out of and they may be directed to the specific airline that has that make of plane, this may also be a flight number for a specific route as well.

This is best done if the complex number is in polar coordinates - that is, a distance from the origin, and an angle. Take the square root of the argument (the absolute value) of the complex number; and half the angle.

It is +1

To find the complex conjugate of a number, change the sign in front of the imaginary part. Thus, the complex conjugate of 14 + 12i is simply 14 - 12i.

Changing a complex number from standard form (x + iy) to normal form r(Cos(theta)+isin(theta)) is relatively simple if you're comfortable with trigonometry and Pythagoras's theorem. It is easiest to imagine it in the context of the complex plane.If you were to draw your complex number on the complex plane, theta would be the angle between the number and the positive x axis, and r would be the length of the line. r is easiest to find; simply put x and y into the equation Sqrt(x2 + Y2)and the result will be r, the length of the complex number.To find theta, you must picture a triangle, imagining the length y to be the opposite, and the length x to be the adjacent, and performing arctan(y/x) to find theta - however, be careful as depending on what quadrant the number is in, you may have to perform further operations in order to find the true angle.

you count the number of boxes IN the shape.

If you understand what the absolute value of a complex number is, skip to the tl;dr part at the bottom. The absolute value can be thought of as a sorts of 'norm', because it assigns a positive value to a number, which represents that number's "distance" from zero (except for the number zero, which has an absolute value of zero). For real numbers, the "distance" from zero is merely the number without it's sign. For complex numbers, the "distance" from zero is the length of the line drawn from 0 to the number plotted on the complex plane. In order to see why, take any complex number of the form a + b*i, where 'a' and 'b' are real numbers and 'i' is the imaginary unit. In order to plot this number on a complex plane, just simply draw a normal graph. The number is located at (a,b). In order to determine the distance from 0 (0,0) to our number (a,b) we draw a triangle using these three points: (0,0) (a,0) (a,b) Where the points (0,0) and (a,b) form the hypotenuse. The length of the hypotenuse is also the "distance" of a + b*i from zero. Because the legs run parallel to the x and y axes, the lengths of the two legs are 'a' and 'b'. By using the Pythagorean theorem, we can find the length of the hypotenuse as (a2 + b2)(1/2). Because the length of the hypotenuse is also the 'distance' of the complex number from zero on the complex plane, we have the definition: |a + b*i| = (a2 + b2)(1/2) ALRIGHT, almost there. tl;dr: Remember that the complex conjugate of a complex number a + b*i is a + (-b)*i. By plugging this into the Pythagorean theorem, we have: b2 = (-b)2 So: (a2 + (-b)2)(1/2) = (a2 + b2)(1/2) QED.

There is no such thing; you seem to have misunderstood something.Any real number can be regarded as a complex number with zero imaginary part, eg.: 5 = 5+0i

The number of pieces for an RC Plane Engine vary on the model of the plane. Here's a link that you may find helpful: http://www.rcairplaneswarehouse.com/

If you are given a plane, you can always find and number of points that are not in that plane but, given anythree points there is always at least one plane that goes through all three.

Here's how you can find any power (fractions would be a root of a number) of any number (complex or real). A real number is a subset of the complex number set, with the imaginary part = 0. I'll refer you to a related link on Euler's formula for information about how this is derived. A complex number can be graphed on the Real-Imaginary plane, with reals on the horizontal axis, and imaginary on the vertical. Convert the complex number from x-y style coordinates in this plane to polar coordinates.For a complex number a + bi, here's how you do that. We will end up with a magnitude and an angle. The magnitude is sqrt(aÂ² + bÂ²). The angle is found by tan-1(b/a). Now to find a power, apply the power to the magnitude (for cube root this is exponent of 1/3). Then multiply the angle by the power (in this case you divide by 3). Really for a cube root there will be 3 distinct roots. Since a the angle of a circle is 360Â° or 2pi radians, you can add 2pi radians to the angle of the original complex number, then divide by 3 to determine the second root. Add 4pi radians to the original angle and then divide by 3 to determine the 3rd root. Then convert back to x-y coordinates if you want to:Magnitude*(cos(angle) + i*sin(angle)), for each of the 3 angles that you determined.See the question: 'Strategy for finding the cube root of complex numbers'Strategy_for_finding_the_cube_root_of_complex_numbers