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Evaluate and express this complex number in standard form the absulote value of 5-12i?
The absolute value of a complex number is it's magnitude (distance from the origin). Think about complex numbers graphically, with reals on the horizontal axis, and imaginaries on the vertical axis. Now you have a right triangle: From the origin move to the right 5 units, then move down 12 units. The absolute value, or magnitude, is the length of the hypotenuse.
For this triangle, it is 13: sqrt(5^2 + 12^2) = sqrt(25+144) = sqrt(169) = 13. For magnitudes, we are only interested in the positive square root.
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