Precalculus, Chapter 6, 6.5, Section 6.5, Problem 9

You need to find the absolute value of the complex number, using the formula |z| = sqrt(a^2+b^2) , hence, you need to determine a and b.
a = 4, b = -6.
Replacing 4 for a and -6 for b in formula of absolute value, yields:
|z| = sqrt(4^2+(-6)^2)
|z| = sqrt(16+36)
|z| = sqrt52 => |z| = 2 sqrt 13
Hence, the distance of the complex number z = 4 - 6i from the origin is given by the aboslute value |z| = 2 sqrt 13 .
The complex number z = 4 - 6i is displayed as the point (4,-6) in a coordinate plane, or as a vector from the origin to the point (4,-6).

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