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Question

If x+iy=(1+i)(1+2i)(1+3i), then x2 + y2 =
(a) 0
(b) 1
(c) 100
(d) none of these

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Solution

(c) 100

x + iy = (1+i)(1+2i)(1+3i)Taking modulus on both the sides:x + iy=(1+i)(1+2i)(1+3i)x + iy= 1+i×1+2i×1+3ix2+y2=12+1212+2212+32x2+y2 = 2510 x2+y2= 100Squaring both the sides, x2+y2 =100

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