0
What is the complex number of its distance for the origin in the complex plane?
Wiki User
∙ 12y ago
This is called the magnitude. It can be found (for a complex number a + bi) as:
(where a & b are both real numbers and i is the imaginary unit)
sqrt(a^2 + b^2)
Wiki User
∙ 12y ago
Add your answer:
Earn +20 pts
The plane formed by the intersection of two number lines?
Origin
Is the square root of 1 an irrational number?
No. An irrational number is still a real number - it lives on the number line.The square root of -1 (known as i) is an imaginary number. It is on the imaginary axis of the complex plane.A number with components from the real axis and the imaginary axis is a complex number, and is on the complex plane.
When the first number in an ordered pair is 0 where is the point located?
The first number in an ordered pair (of rectangular coordinates) is the distance from the origin along the x- axis. If the number is 0, then any point having this coordinate must lie on the y-axis. If the second number is 0 then the point is at the origin (0,0). If the second number is positive then the point lies on the y-axis above the origin. If the second number is negative then the point lies on the y-axis below the origin.
What is the ordered pair for the origin of the coordinate plane?
Origin = (0,0)
Explain about Cartesian coordinate system?
In 2-dimensions, the Cartesian coordinate system comprises a pair of axes meeting at right angles at a point called the origin. Conventionally the axes are identified as the x-axis (going from left to right) and the y-axis (going from the bottom to the top).Every point of the Cartesian plane is allocated an ordered pair of numbers, called coordinates. The first number (abscissa) represents the distance of the point to the right of the origin and the second (ordinate) represents the distance in the upward direction. If the point is to the left or below the origin then the corresponding coordinate is negative.
What is the trigonometric form of a complex number?
The standard form of a complex number is the cartesian one; a plane with orthogonal axes for real parts and imaginary parts. A complex number has a pair of co-ordinates defining its position on the plane. A trigonometric form is a plane with an origin, and one line from the origin to infinity. A complex number is defined by its distance from the origin and the angle between the datum line and the line joining the number to the origin. It is just like co-ordinate geometry with co-ords r, theta instead of x,y.
In a number plane what is the zero called?
See http://en.wikipedia.org/wiki/Complex_numberIn the complex number plane, it would be called the Origin, which has coordinates of (0, 0i)
Is there any way to calculate the absolute value of a complex number that equals a negative number?
Given that absolute values are always positive, and that there is no equivalence between complex numbers and real numbers, I would have to say no, there isn't. The absolute value of a real number is its distance from zero on a number line. Since a distance is always positive, we say the absolute value is always positive. Graphically, a real number is just a point on a number line. The absolute value of a complex number is its distance form the origin in a coordinate plane, where coordinate axes are the x-axis with real numbers, and the y-axis with imaginary numbers. In this diagram, called Argand diagram, a complex number a + bi (where a and b are real numbers) is the point (a, b) or the vector from the origin to the point (a, b). Using the distance formula, the absolute value or the distance of a complex number a + bi is equal to the principal square root of (a2 + b2).
What are the characteristics of a coordinate plane?
It is a plane surface with an origin and a pair of orthogonal axes. The location of any point in the plane is given by an ordered pair of coordinates: the abscissa (distance to the right of the origin) and the ordinate (distance in the vertical direction from the origin).
What is mode of z in complex no?
In complex mode functions, modules, and procedures cannot operate. For a complex number z = x + yi, first define the absolute value. This would be |z| and is the distance from z to 0 in the complex plane.
How many numbers have an absolute value equal to 5?
on the real number line there are 2 values with |5|, ie +5 and -5. on the complex plane there are an infinite set of values with an absolute value of 5, ie all the points of distance 5 from the origin.
Find the complex number that is farthest away from the complex plane?
All complex numbers are part of the "complex plane", so none of them is farther than others.
On a number plane zero is called?
The origin.
What do you call a mysterious bright starlike object in the galaxy core?
A region in the complex number plane such that the line segment joining any of its points to the origin lies entirely in the region.
The plane formed by the intersection of two number lines?
Origin
What does absolute vaule mean?
The absolute value of a number (in any dimension) is the positive distance between that number and the origin. For ordinary, real numbers, absolute value is simple; e.g. |5| = 5 and |-4.3| = 4.3. For complex numbers in the form a + bi, the "absolute value" is also the length from that point on the plane to the origin, which, by the Pythagorean theorem, is sqrt(a2 + b2). For example, |4 + 3i| = sqrt(42 + 32) = 5.
Why are the absolute values of a complex number and its conjugate always equal?
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.
