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If z= x- iy and z^3 = p+IQ then x÷p+ y÷q÷p^2 + q^2 is equal to

If z= x- iy and z^3 = p+IQ then x÷p+ y÷q÷p^2 + q^2 is equal to

Grade:12th pass

2 Answers

Arun
25750 Points
4 years ago
Z=x+iy and z¹/³=p+iq
∴, (x+iy)¹/³=p+iq
Cubing both sides,
x+iy=(p+iq)³
or, x+iy=p³+3p²iq+3p(iq)²+(iq)³
or, x+iy=p³+3ip²q-3pq²-iq³  [i²=-1]
or, x+iy=(p³-3pq²)+i(3p²q-q³)
Equating the real and imaginary parts from both sides,
x=p³-3pq² and y=3p²q-q³
∴, (x/p+y/q)/(p²+q²)
=[(p³-3pq²)/p+(3p²q-q³)/q]/(p²+q²)
=(p²-3q²+3p²-q²)/(p²+q²)
=(4p²-4q²)/(p²+q²)
=4(p²-q²)/(p²+q²)
 
 
Saurabh Koranglekar
askIITians Faculty 10335 Points
4 years ago
Dear student

Please repost using brackets, that it is clear what the exact question is

However
P = (cube(x)) - ((3x)*(sqr(y)))
Q = (cube(y)) - ((3y)*(sqr(x)))

Regards

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