Suppose x,y,p and q are real numbers and the inverse element for multiplication of the complex number x+yi is 5-11i.
If (5-11i)^2 * (x+yi)^3 = p+qi, the value of p+q can be expressed as a/b. What is the value of a and b?
1/(5-11i) = 1/√146 (5+11i)
(5-11i)^2 * (x+yi)^3
= [(5-11i)^2 * (x+yi)^2] * (x+yi)
But we know that (5-11i)(x+yi) = 1, so
= x+yi
= 1/√146 (5+11i)
p+q = 5/√156 + 11/√146 = 16/√146