Question

Find the value of x and y if :1. (x - 2y) + 3yi = 4- 6i 2. [ 2/3x - 3/4y] + 5/6yi = 1 - 2i

Answer 1

1. (x-2y)+3yi=4-6i
or, x-2y+3yi-4+6i=0
or, (x-2y-4)+i(3y+6)=0
Equating the real and imaginary part we have,
x-2y-4=0
or, x-2y=4 and
3y+6=0
or, 3y=-6
or, y=-2
∴, x=4+2y
or, x=4+2×(-2)
or, x=4-4
or, x=0
∴, x=0, y=-2 Ans.

2. (2/3x-3/4y)+5/6yi=1-2i 
or, (8x-9y+10yi)/12=1-2i
or, 8x-9y+10yi=12-24i
or, (8x-9y-12)+i(10y+24)=0
Equating the real and imaginary part we have,
8x-9y-12=0 and
10y+24=0
or, 10y=-24
or, y=-24/10
or, y=-12/5
∴, 8x-9×(-12/5)-12=0
or, 8x+108/5-12=0
or, 8x+(108-60)/5=0
or, 8x=-48/5
or, x=-48/5×1/8
or, x=-6/5
∴, x=-6/5, y=-12/5 Ans.