Short Answer TypeIf (a + ib) (c+id)(e+if)(g+ih) = A+iB, then show that : (a2 + b2) (c2 + d2 ) (e2 + f2 ) (g2Â h2 ) = A2 + B2
Find the values of x and y, if.
(2x + y - 5) + (3x - 2y - 4) i = 0
(2x + y - 5) + (3x - 2y - 4) i = 0
Equating real and imaginary parts, we get
Re (z) : 2x + y - 5 = 0Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â ...(i)
Im (z) : 3x - 2y -4 = 0Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â ...(ii)
Â
Multiplying (1) b y 3 and (ii) by 2, we get\
6x + 3y - 15 = 0Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â ...(iii)
6x - 4y - 8Â = 0Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â ...(iv)
Subtracting (iv) from (iii), we get
             7y - 7 = 0                          
            y = 1
Using in (i), we get
             2x + 1 - 5 = 0                    
                         x = 2
Hence,  x = 2 and y = 1
   Â
are two different complex number with 
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