Question

if x+2i+15i`6y=7x+i`3(y+4) find x+y.​

Answer 1

Answer:

x + y = 9

Step-by-step explanation:

x + 2i  + 15i⁶y = 7x  + i³(y + 4)

=> x + 2i  + 15i⁴.i² y  = 7x  - i(y + 4)

=> x + 2i  - 15y = 7x - i(y + 4)

=> (x - 15y) + 2i  = 7x  + i (-(y + 4))

Equating real & imaginary part

x - 15 y = 7x

=> 6x = -15y

=> 2x = -5y

y + 4 = - 2

=> y = -6

=> 2x = -5(-6)

=> x = 15

x + y = 15 - 6 = 9

Answer 2

Answer:

=> x + 2 ( i ) + 15 y ( i )^6 = 7 x + ( y + 4 ) ( i )^3

We know that in such an equation, real part on the left side must be equal to real part on the right hand side of the equation. The same rule is applicable for the imaginary parts.

Hence comparing the real parts we get ---

=> x - 15 y = 7 x

=> 6 x = -- 15 y ..................... (1)

And comparing the imaginary parts we get ---

=> y = 4 = 2

=> y = -- 2 ............... (2)

From (1) and (2) we get --

=> 6 x = -- 15 y

=> 6 x = -- 15 ( -- 2 )

=> x = 5

Hence ( x + y ) = 5 + ( -- 2 ) = 3 ..................... Answer