Asked by CHRIS
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?
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?
Answers
Answered by
Steve
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
(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
There are no AI answers yet. The ability to request AI answers is coming soon!
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.