Complex or Simplex?
− 1 + − 4 + − 1 6 + − 6 4 + … ⋅ − 1 − − 4 − − 1 6 − − 6 4 − … The expression above can be written as a + b i , where a , b are real numbers .
Find the value of a + b .
Clarification:
i
=
−
1
.
The answer is -2.
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1 solution
I'm sorry, i know that the value of the expression is -2, but does it mean that the value of a + b is -2? The problem ask about the value of a + b . So, i think a + b = − 2
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@Fidel Simanjuntak , as the expression equals − 2 and can be written as a complex number, we have a + b i = − 2 and so we know b = 0 ∧ a = − 2 ⇒ a + b = − 2
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Oh, okay.. I didn't concern that b = 0 .. Hahahahaha
I'm sorry to be 3 years and a half late, but a = − 2 and b = 0 , so we're asked about a + b = − 2 + 0 = − 2
x + 1 = x 2 + 2 x + 1 = x 2 + 4 x 2 + 4 x + 1 = x 2 + 4 x 2 + 1 6 x 2 + 8 x + 1 = x 2 + 4 x 2 + 1 6 x 2 + 6 4 x 2 + … And x − 1 = x 2 − 2 x + 1 = x 2 − 4 x 2 − 4 x + 1 = ⋯ = x 2 − 4 x 2 − 1 6 x 2 − 6 4 x 2 − … So, replacing x = i we can find out that the expression is the same that ( i + 1 ) ( i − 1 ) = i 2 − 1 = − 2