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gulaghasi [49]
3 years ago
11

If z=3−5i, find |z|.

Mathematics
1 answer:
geniusboy [140]3 years ago
5 0

Answer:

Step-by-step explanation:

The absolute value of z is the distance between the point graphed from the complex number and the origin on a complex plane.  In a complex plane, the x axis is replaced by R, real numbers, and the y axis is replaced by i, the complex part of the complex number.  Our real number is positive 3 and the complex number is -5, so we go to the right 3 and then down 5 and make a point.  Connect that point to the origin and then connect the point to the x axis at 3 to construct a right triangle that has a base of 3 and a length of -5.  To find the distance of the point to the origin is to find the length of the hypotenuse of that right triangle using Pythagorean's Theorem.  Therefore:

|z|=\sqrt{(3)^2+(-5)^2} and

|z|=\sqrt{9+25} and

|z|=\sqrt{34}

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