(a+bi)(2+3i)-i=(-11+5i)(1-i)
2a+3ai+2bi+3bi²-i=-11+11i+5i-5i²
2a+(3a+2b-1)i-3b=-11+16i+5
(2a-3b)+(3a+2b-1)i=-6+16i
Therefore; we have the next system of equations:
2a-3b=-6
3a+2b-1=16
Finally, the system of equations is:
2a-3b=-6
3a+2b=17
We can solve this system of equations by reduction method
2(2a-3b=-6)
3(3a+2b=17)
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13a=39 ⇒a=39/13=3
3(2a-3b=-6)
-2(3a+2b=17)
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-13b=-52 ⇒ b=52/13=4
Answer: a=3; b=4
Answer:
Men: 18%
Women: 42%
Boys: 18%
Girls: 22%
Children: 40%
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