if x+yi²=u +iv then show that u/x +v/y =4(x²-y² )
Answers
Answered by
1
Answer:
Given, (x+iy)
3
=u+iv
x
3
+(iy)
3
+3.x.iy(x+iy)=u+iv
x
3
+i
3
y
3
+3x
2
yi+3xy
2
i
2
=u+iv
x
3
−iy
3
+3x
2
yi−3xy
2
=u+iv
(x
3
−3xy
2
)=i(3x
2
y−y
3
)=u+iv
On equating real and imaginary parts, we get
u=x
3
−3xy
2
,v=3x
2
y−y
3
∴
x
u
+
y
v
=
x
x
3
−3xy
2
+
y
3x
2
y−y
3
=
x
x(x
2
−3y
2
)
+
y
y(3x
2
−y
2
)
=x
2
−3y
2
+3x
2
−y
2
=4x
2
−4y
2
=4(x
2
−y
2
)
Answered by
0
Answer:
4(1) –x= 0
x= 4
x= 4 and y= 1
Take this answer and write it
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