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18) Ifx+iy= (a+ib)3, show that x/a+y/b=4(a2-b2)​

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Step-by-step EXPLANATION:

= x + iy = {(a + ib)}^{3} \\ = x + iy = {a}^{3} + {i}^{3} {b}^{3} + 3aib(a + ib) \\ = x + iy = {a}^{3} - i{b}^{3} + 3i {a}^{2} b - 3a {b}^{2} \\ = x + iy = ({a}^{3} - 3a {b}^{2} ) \: + i(3 {a}^{2} b - {b}^{3} ) \\ on \: comparing \: on \: both \: sides \\ x = {a}^{3} - 3a {b}^{2} ,\: \: y = 3 {a}^{2}b - {b}^{3} \\ \frac{x}{a} = {a}^{2} - 3 {b}^{2} , \: \: \frac{y}{b} = 3 {a}^{2} - {b}^{2} \\ \frac{x}{a} + \frac{y}{b} = {a}^{2} - 3 {b}^{2} + 3 {a}^{2} - {b}^{2} \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 4 {a }^{2} - 4 {b}^{2} = 4( {a}^{2} - {b}^{2} )

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