If ( x + iy ) ( 3 – 4i ) = (5 + 12i ) , then root of(x2\xa0+ y2) =??\xa0

If ( x + iy ) ( 3 – 4i ) = (5 + 12i ) , then root of(x2\xa0+ y2) =??

1.	If ( x + iy ) ( 3 – 4i ) = (5 + 12i ) , then root of(x2\xa0+ y2) =??\xa0
Answer» Given: ( x + iy ) ( 3 – 4i ) = (5 + 12i )Solution:( x + iy ) =\xa0(5 + 12i ) /\xa0( 3 – 4i )By Rationalization,\xa0( x + iy ) =\xa0(5 + 12i ) /\xa0( 3 – 4i ) ×\xa0( 3 +\xa04i )/\xa0( 3 +\xa04i )=\xa0(5 + 12i )\xa0( 3 +\xa04i )\xa0/\xa0( 3 +\xa04i )\xa0( 3 -\xa04i )= (15 + 36i + 20i +\xa048i2)\xa0/\xa03^2 - (4i)2 {( 3 +\xa04i )\xa0( 3 -\xa04i )\xa0=\xa032 - (4i)2 because (a+b)(a-b)=a2 - b2}= (15 - 48 + 56i)\xa0/\xa09 - 16i2 (48i^2 = -48 because i2 = -1)= ( -33 + 56i)\xa0/\xa09 +16= ( -33 + 56i)\xa0/\xa025So, ( x + iy ) = -33/25\xa0+ 56i/25\xa0And, ( x -\xa0iy ) = -33/25 -\xa056i/25\xa0Now,\xa0( x + iy )( x -\xa0iy ) = (-33/25\xa0+ 56i/25 )\xa0(-33/25 -\xa056i/25 )x2\xa0+ y2\xa0=\xa0(-33/25)2\xa0- (56i/25)2= 1089/625 - 3136 i2/\xa0625= 1089/625 +\xa03136 /\xa0625= 4225\xa0/\xa0625 = 6.76Now Root of\xa0x2\xa0+ y2\xa0means root of\xa06.76 = 2.6 (Answer)