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Why is it useful for me to know the absolute value of a number?
The absolute value of a number is the distance to zero. When adding which ever number has the greater absolute value will determine the sign of the answer.
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.
How do you determine the absolute value of a integer?
The absolute value of a number is expressed with the symbol |. To show you want to find the absolute value of an integer(using x as the integer) you would do this |x|. Examples- |2| = 2 |-9| = 9 |325| = 325 |-457245| = 457245
Find the absolute value of the complex number z equals 3 plus 4i?
('|x|' = Absolute value of x) |3+4i| = √(32 + 42) = √(9+16) = √25 = 5 Thus |3+4i| = 5.
What is the absolute value for -7.11?
Absolute value for -7.11 is 7.11.
Which operation involves complex numbers requires the use of a conjugate to be carried out?
One operation that is used a lot in quantum mechanics is taking the absolute value of the square of a complex number. This is equivalent to multiplying the complex number by its complex conjugate - and doing this is simpler in practice.
What is the absolute value of a complex number?
The absolute value of a complex number a+bi is the square root of (a2+b2). For example, the absolute value of 4+9i is the square root of (42 + 92) which is the square root of 97 which is about 9.8489 (The absolute value of a complex number is not complex.)
What is another name for absolute value of a complex number?
The absolute value of a complex number is the magnitude of the number, which is found from sqrt(a² + b²) for the complex number a + bi
Which arithmetic operation requires the use of complex conjugate?
It can be used as a convenient shortcut to calculate the absolute value of the square of a complex number. Just multiply the number by its complex conjugate.I believe it has other uses as well.
What is the absolute value of -4.2?
The absolute value of a number is the distance from that number to 0. Therefore, the absolute value is ALWAYS positive. the absolute value of -4.2 is 4.2 To find the absolute value, just determine how far it is from 0.
Why is it useful for me to know the absolute value of a number?
The absolute value of a number is the distance to zero. When adding which ever number has the greater absolute value will determine the sign of the answer.
Can absolute value be zero?
The absolute value of zero is zero. The absolute value of any other real number - or even of any other complex number - is different from zero.
Can an absolute value be zero?
The absolute value of zero is zero. The absolute value of any other real number - or even of any other complex number - is different from zero.
A numbers distance from zero?
That is called the "absolute value". For example, the absolute value of 5 is 5; the absolute value of -5 is also 5. If you are familiar with complex numbers, the absolute value of 4 + 3i, for example, is also 5.
Why cant the adsolute value of a number be negtive?
That is because of the way the absolute value is defined. The absolute value of a positive number is positive, the absolute value of a negative number is also positive. The absolute value of zero is zero. Even in the complex numbers, the absolute value is defined in such a way that it is a real and positive number.
How do you determine the absolute value of a number?
To find the absolute value of a number count the amount of spaces it is away from Zero. If the number is 5 then the absolute value is 5. If the number is -5 then the absolute value is 5. And so on and so forth.
How do you rationalise the denominator?
It depends on what the denominator was to start with: a surd or irrational or a complex number. You need to find the conjugate and multiply the numerator by this conjugate as well as the denominator by the conjugate. Since multiplication is by [conjugate over conjugate], which equals 1, the value is not affected. If a and b are rational numbers, then conjugate of sqrt(b) = sqrt(b) conjugate of a + sqrt(b) = a - sqrt(b), and conjugate of a + ib = a - ib where i is the imaginary square root of -1.
