Find the number of non-zero integral solutions of the equation 1-i -2-If -a - ib- -c - id- -e - if- -g ih- A - iB- then show that-a-b2- -c2 - d- -e2 -f2- -g-h- - A2 - B2

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Equation of a Plane : Intercept Form

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Question

Find the number of non-zero integral solutions of the equation 1-i =2\ast.If (a + ib) (c + id) (e + if) (g ih) A + iB, then show that(a+b2) (c2 + d) (e2 +f2) (g+h) = A2 + B2

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\frac{(a + i b)}{(c + i d)} = x + i y

\frac{a - i b}{c - i d} = x - i y

\frac{a^{2} + b^{2}}{c^{2} + d^{2}} = x^{2} + y^{2}

(a + i b) (c + i d) (e + i f) (g + i h) = A + i B

(a^{2} + b^{2}) (c^{2} + d^{2}) (e^{2} + f^{2}) (g^{2} + h^{2}) =

\frac{a + i b}{c + i d} = p + i q

\frac{a - i b}{c - i d} = p - i q

p^{2} + q^{2} = \frac{a^{2} + b^{2}}{c^{2} + d^{2}}

a, b, c, d, e, f, g, h

a^{2} + d^{2} + f^{2} + g^{2} = b^{2} + c^{2} + e^{2} + h^{2}

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