Final answer:
To find the product Q · E · D, the complex numbers are multiplied step by step. The product of Q and E is 146, and multiplying this result by D gives the final answer of 292i.
Step-by-step explanation:
The question asks to find the product of the complex numbers Q, E, and D. To find the product Q · E · D, we multiply these complex numbers step by step.
Given numbers are Q = 11 - 5i, E = 11 + 5i, and D = 2i.
Firstly, we find the product of Q and E:
- Q · E = (11 - 5i)(11 + 5i)
- = 11· 11 + 11 · 5i - 5i · 11 - 5i · 5i
- = 121 + 55i - 55i - 25i²
- Since i² = -1, this simplifies to:
- = 121 + 0 - 25(-1)
- = 121 + 25
- = 146
Now we multiply this result by D:
- (Q · E) · D = 146 · 2i
- = 292i