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10.08.2008 · Absolute value of imaginary numbers? Hi, Here's something that stumped my pre-calculus teacher. Supposedly, the absolute value of an imaginary number such as 4 + 3i is found by throwing away the i and using the pythagorean theorem on it. i.e. sqrt ( 4^2 + 3^2 ) = 5 So according to that formula, if you have 3 numbers: x = 4 + 3i y = 3 + 4i

Keywords: problem; absolute value; complex numbers; pythagorean theorem; complex plane; distance from ...

have the same absolute value. ... where Re(z) = x and Im(z) = y denote the real and imaginary parts of z, respectively. When the imaginary ...

The absolute value of a complex number a + bi, also called the modulus of a complex number a + bi, is its distance from the origin on the complex number plane.

The absolute value of complex number is also a measure of its distance from zero. However, instead of measuring this distance on the number line, a complex number's absolute value is measured on the complex number plane.

Absolute Value The absolute value (or modulus) of a real number is the corresponding nonnegative value that disregards the sign. For a real value, a, the absolute value is: a, if a is greater than or equal to zero -a, if a is less than zero abs (-0) returns 0. Complex Magnitude

Jun 06, 2021 · The absolute value(Modulus) of a number is the distance of the number from zero. Absolute value is always represented in the modulus(|z|) and its value is always positive. So, the absolute value of the complex number Z = a + ib is |z| = √ (a 2 + b 2) So, the absolute value of the complex number is the positive square root of the sum of the square of real part and the square of the imaginary part, i.e., Proof:

The unit circle. Some complex numbers have absolute value 1. Of course, 1 is the absolute value of both 1 and –1, but it's also the absolute value of both i and – i since they're both one unit away from 0 on the imaginary axis. The unit circle is the circle of radius 1 centered at 0.

For a complex number z = x + yi, we define the absolute value |z| as being the distance from z to 0 in the complex plane C. This will extend the definition of ...

The distance formula says the distance from the original to any point (x,y) is sqrt(x 2 + y 2), so the absolute value of 3+4i = sqrt(3 2 + 4 2) = 5. Notice that when you have a complex number with no imaginary part (such as 4+0i), the absolute value is the positive square root of the real part squared - in other words, the absolute value of the real part.

Of course, 1 is the absolute value of both 1 and –1, but it's also the absolute value of both i and –i since they're both one unit away from 0 on the imaginary axis. The unit circle is the circle of radius 1 centered at 0. It include all complex numbers of absolute value 1, so it has the equation |z| = 1. A complex number z = x + yi will lie on the unit circle when x 2 + y 2 = 1.

The absolute value of complex number is also a measure of its distance from zero. However, instead of measuring this distance on the number line, a complex number's absolute value is measured on the complex number plane.

Notice that when you have a complex number with no imaginary part (such as 4+0i), the absolute value is the positive square root of the real part squared - in other words, the absolute value of the real part. So this "distance" method is just an extension of what you already use for real numbers. Hope this explanation helps, Stephen La Rocque. and,

The absolute value of complex number is also a measure of its distance from zero. However, instead of measuring this distance on the number line, a complex ...

Complex numbers consist of real numbers and imaginary numbers. Hence, unlike integers, it is difficult to find the absolute value for them. Suppose, x+iy is the given complex number. z = x+iy. The absolute value of z will be; |z|= √ [Re (z) 2 +Im (z) 2 ] |z| = √ (x 2 +y 2) Where x and y are the real numbers.

Yes, if is an imaginary number (with being a real number), then its absolute value is the absolute value of . 176 views ...