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If ( x + iy ) …

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

 

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  • 1 answers

Manish Gandhi 7 years, 3 months 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 ) = -33/25 + 56i/25 

And, ( x - iy ) = -33/25 - 56i/25 

Now, ( x + iy )( x - iy ) = (-33/25 + 56i/25 ) (-33/25 - 56i/25 )

x+ y2 = (-33/25)2 -  (56i/25)2

= 1089/625 - 3136 i2/ 625

= 1089/625 + 3136 / 625

= 4225 / 625 = 6.76

Now Root of x+ ymeans root of 6.76 = 2.6 (Answer)

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