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If the set R = \(a, b) : a + 5b = 42, a, b N\ has m elements and n=1m (1 - in! ) = x + iy, where i = -1, then the value of m + x + y is
(1) 12
a = 42 - 5b 1 gives b = 1, 2, , 8 (with a = 37, 32, , 2), so m = 8
i1! = i, i2! = i2 = -1, i3! = i6 = -1
For n 4, n! is a multiple of 4, so in! = 1 and 1 - in! = 0
n=18 (1 - in! ) = (1 - i) + 2 + 2 + 0 = 5 - i
x = 5, y = -1
m + x + y = 8 + 5 - 1 = 12
Answer: (1)
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