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?

Guest Dec 5, 2020

#1**+1 **

"*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.

Alan Dec 5, 2020