If ( x + iy ) …
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Manish Gandhi 9 years ago
Given: ( x + iy ) ( 3 – 4i ) = (5 + 12i )
Solution:
( x + iy ) = (5 + 12i ) ( 3 – 4i )
By Rationalization, ( x + iy ) = (5 + 12i ) ( 3 – 4i ) ( 3 + 4i ) ( 3 + 4i )
= (5 + 12i ) ( 3 + 4i ) ( 3 + 4i ) ( 3 - 4i )
= (15 + 36i + 20i + 48i2) 3^2 - (4i)2 {( 3 + 4i ) ( 3 - 4i ) = 32 - (4i)2 because (a+b)(a-b)=a2 - b2}
= (15 - 48 + 56i) 9 - 16i2 (48i^2 = -48 because i2 = -1)
= ( -33 + 56i) 9 +16
= ( -33 + 56i) 25
So, ( x + iy ) = -3325 + 56i25
And, ( x - iy ) = -3325 - 56i25
Now, ( x + iy )( x - iy ) = (-3325 + 56i25 ) (-3325 - 56i25 )
x2 + y2 = (-3325)2 - (56i25)2
= 1089625 - 3136 i2 625
= 1089625 + 3136 625
= 4225 625 = 6.76
Now Root of x2 + y2 means root of 6.76 = 2.6 (Answer)
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