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)`.

Answer 1

`|(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