Ramanujan and Hardy played a game where they both picked a complex number. If the product of their numbers was 17 - 20i, and Hardy picked 7 - 2i, what number did Ramanujan pick?
+33615 "Ramanujan and Hardy played a game where they both picked a complex number. If the product of their numbers was 17 - 20i, and Hardy picked 7 - 2i, what number did Ramanujan pick?"
Let Ramanujan number be a + bi, then
(a + bi)*(7 - 2i) = 17 - 20i
7a - 2ai + 7bi + b = 17 - 20i
Equate real and imaginary parts:
7a + b = 17
-2a + 7b = -20
Solve these two equations for a and b.
