Question

Find x and y if `|(4"i", "i"^3, 2"i"),(1, 3"i"^2, 4),(5, -3, "i")|` = x + iy where i² = – 1

Answer 1

`|(4"i", "i"^3, 2"i"),(1, 3"i"^2, 4),(5, -3, "i")|`  

= `|(4"i", "i"^3, 2"i"),(1, 3"i"^2, 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