How do you find the absolute value of the complex number?

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1 Answer
George C.
May 24, 2015

If #z = a+ib# where #a, b in RR# then #|z| = |a+ib| = sqrt(a^2+b^2)#

To picture this, think of #a+ib# as a point #(a, b)# in the plane.
The modulus is the distance of that point from the origin #(0,0)#.

We can calculate the distance by dropping a perpendicular onto the real axis at #(a, 0)# and using the Pythagorean Theorem on the right angled triangle formed by these three points, which has sides of length #a#, #b# and #sqrt(a^2+b^2)#.

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