SOLUTION: Question: The absolute value of a complex number z = a + bi, denoted |z|, is given by the formula |z| = √a^2 + b^2 Find three distinct complex numbers (which are neither pur

Algebra ->  Complex Numbers Imaginary Numbers Solvers and Lesson -> SOLUTION: Question: The absolute value of a complex number z = a + bi, denoted |z|, is given by the formula |z| = √a^2 + b^2 Find three distinct complex numbers (which are neither pur      Log On


   

Question 1066938: Question: The absolute value of a complex number z = a + bi, denoted |z|, is given by the formula |z| = √a^2 + b^2
Find three distinct complex numbers (which are neither purely imaginary nor purely real) such that each has an absolute value of 5.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
(1) +z+=+3+%2B+4%2Ai+
(2) +z+=+4+%2B+3%2Ai+
(3) +z+=+3+-+4%2Ai+
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check:
(3)
+z+=+3+-+4%2Ai+
+abs%28+z+%29+=+abs%28+3+-+4%2Ai+%29+
+sqrt%28+3%5E2+%2B+%28-4%29%5E2+%29+=+sqrt%28+9+%2B+16+%29+
+sqrt%28+9+%2B+16+%29+=+sqrt%28+25+%29+
+abs%28z%29+=+5+
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You can check (1) and (2)