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Derivative of One Function w.r.t Another

If x+i y3=u+i...

Question

If (x + iy)³ = u + iv, then show that.

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Solution

On equating real and imaginary parts, we obtain

Hence, proved.

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Similar questions

If $(x + i y)^{3} = u + i v$ , then show that $\frac{u}{x} + \frac{u}{y} = 4 (x^{2} - y^{2})$

(x + i y)^{3} = u + i v

, then prove that

\frac{u}{x} + \frac{v}{y} = 4 (x^{2} - y^{2})

u + i v = (x + i y)^{3}

\frac{u}{x} + \frac{v}{y} =

u + i v = (x + i y)^{3}

\frac{u}{x} + \frac{v}{y} =

(x + y i)^{3} = u + v i,

\frac{u}{x} + \frac{v}{y} = 4 (x^{2} - y^{2}) .

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