Question

let a= the number of distinct arrangements of the letters in the word GLASSES and b= the radius of the circle with equation x^2+y^2-8x-2y+16=0, find the value of i^a times i^b times i^ab where i=root -1

Answer 1

@Hero please help

Answer 2

i know that glasses has 7 letters

Answer 3

\[\huge a=7!,b=1\]
\[\huge i^ai^bi^{ab}=i^{a+b+ab}=i^{7+1}=1\]

Answer 4

thats all?

Answer 5

yeah i guess

Answer 6

thank you

Answer 7

Not all those are unique, though @Jonask. For example, "bss" only has 3 UNIQUE possibilities: bss,sbs and ssb. The other three possibilities are redundant, so it shold be \(\dbinom{3}{2}\) for this case.