Question

if (x+iy) (p+iq) =(x2+y2) then ,x =_____​

Answer 1

Answer:

On expansion of LHS

(xp-yq) + (xq+yp)i = (x^2+y^2)i

On comparing real parts

x = yq/p

In comparison of imaginary parts

xq+ yp = x^2+y^2

Put tge value of x = yq/p

y = p

Hence x = q

Answer 2

Please mind the upper and lower cases of letters.

I am taking all of them in lower case.

So given (x+iy)(p+iq) = (x^2 + y^2)i

=> px - qy + i(qx + py) = (x^2 + y^2)i

=> px - qy = 0 and qx + py = x^2 + y^2

p = y and q= x satisfy both the equations.