SOLUTION: Solve for x and y, 3x + iy = (1 + i)(x^2 + y^2). Ans: x = 3/10 and y = 9/10

Algebra ->  Complex Numbers Imaginary Numbers Solvers and Lesson -> SOLUTION: Solve for x and y, 3x + iy = (1 + i)(x^2 + y^2). Ans: x = 3/10 and y = 9/10      Log On


   

Question 1113675: Solve for x and y, 3x + iy = (1 + i)(x^2 + y^2). Ans: x = 3/10 and y = 9/10
Answer by math_helper(2461) About Me  (Show Source):
You can put this solution on YOUR website!
+3x+%2B+yi+=+%281%2Bi%29%28x%5E2%2By%5E2%29+
Let +k=x%5E2%2By%5E2+ for now:
++3x%2Byi+=+%281%2Bi%29k+
++3x%2Byi+=+k%2Bki+

Using Re{LHS} = Re{RHS}, Im{LHS}=Im{RHS} :
3x = k  —>  x = k/3  (1)
y = k                (2)

But +x%5E2%2By%5E2+=+k+ so, using (1) and (2):
+k%5E2%2F9+%2B+k%5E2++=+k+
++10k%5E2+-+9k+=+0+
k=0 and/or k=9/10
k=0 is a trivial solution (x=y=k=0)
k=9/10 —> +highlight%28+x+=+3%2F10%29+ , +highlight%28++y+=+9%2F10%29+