SOLUTION: Find two complex numbers whose sum equals 15 and whose product equals 90. How would I go about putting it into the format z=___ +- ___i ???? Any help would be greatly appreciated

Algebra ->  Complex Numbers Imaginary Numbers Solvers and Lesson  -> Lesson -> SOLUTION: Find two complex numbers whose sum equals 15 and whose product equals 90. How would I go about putting it into the format z=___ +- ___i ???? Any help would be greatly appreciated      Log On


   



Question 684433: Find two complex numbers whose sum equals 15 and whose product equals 90. How would I go about putting it into the format z=___ +- ___i ???? Any help would be greatly appreciated
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
To end up with only real numbers for product and sum,
the complex numbers have to be of the form
+a+%2B+b%2Ai+ and +a+-+b%2Ai+
given:
+a+%2B+b%2Ai+%2B+a+-+b%2Ai++=+2a+
+2a+=+15+
+a+=+7.5+
and
+%28+7.5+%2B+b%2Ai+%29%2A%28+7.5+-+b%2Ai+%29+=+90+
+56.25+-+b%5E2%2Ai%5E2+=+90+
+56.25+-+b%5E2%2A%28-1%29+=+90+
+b%5E2+=+90+-+56.25+
+b%5E2+=+33.75+
+b+=+5.8095+
The complex numbers are:
+7.5+%2B+5.8095%2Ai+ and
+7.5+-+5.8095%2Ai+
check:
+%28+7.5+%2B+5.8095%2Ai+%29%2A%28+7.5+-+5.8095%2Ai+%29+
+7.5%5E2+-+5.8095%5E2%2Ai%5E2+
+56.25+-+33.7503%2A%28-1%29+
+56.25+%2B+33.7503+=+90.0003+
close enough