The magnitude of a point in a coordinate system is the distance of that point from zero.^{[1]} For real numbers, the magnitude is also called the absolute value. Magnitude (and absolute value) are written using a vertical line '|'.
The magnitude of x is written |x|. The magnitude of -7 is written |-7|.
Figure 1: Number line showing that 3 and -3 are both a distance of 3 from zero. |
The number line in figure 1 shows that both the numbers 3 and -3 are a distance of 3 from zero.
The magnitude of a vector <-3, 4> is calculated using the distance formula: .
The definition of magnitude is given as the distance of a number from zero. For complex numbers, the definition holds. Use the distance formula , where a is the length of one leg from zero and b is the length of the other leg from zero.
Take the complex number 4+3i. Figure 2 shows what this point looks like when plotted
on the complex plain.
Figure 2: The complex number 4 + 3i plotted on the complex plane |
Note that magnitude is always positive or zero. It can never be negative.
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