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Question
Find x and y if `|(4"i", "i"^3, 2"i"),(1, 3"i"^2, 4),(5, -3, "i")|` = x + iy, where i = `sqrt(-1)`.
Solution
`|(4"i", "i"^3, 2"i"),(1, 3"i"^2, 4),(5, -3, "i")|`
= `|(4"i", -"i", 2"i"),(1, -3, 4),(5, -3, "i")|` ...[∵ i2 = – 1]
= `4"i"|(-3, 4),(-3, "i")| - (- "i")|(1, 4),(5, "i")| + 2"i"|(1, -3),(5, -3)|`
= 4i(– 3i + 12) + i(i – 20) + 2i(– 3 + 15)
= – 12i2 + 48i + i2 – 20i + 24i
= – 11i2 + 52i
= – 11(– 1) + 52i ...[∵ i2 = – 1]
= 11 + 52i
Comparing with x + iy, we get
x = 11, y = 52
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