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Sum of Infinite Terms

For two compl...

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For two complex numbers z and w it is given that (|z|^2)w — (|w|^2)z = z —w holds. Then show that either z=w or zw* =1 where w* is the conjugate of w.

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Q. For complex numbers

z

w

{| z |}^{2} w - {| w |}^{2} z = z - w

z = w

z ¯ w = 1

Q. If z and w be two complex numbers, such that

| z |^{2} w - | w |^{2} z = z - w

(z \neq w),

Z

W

are two complex numbers such that

¯ z + i ¯ w = 0

a r g (z w) = π

a r g (Z) =

z

w

be two complex numbers such that

| z | \leq 1, | w | \leq 1

| z + i w | = | z - i ¯ ¯¯ ¯ w | = 2,

z

w

are two complex numbers such that

| z w | = 1

a r g (z) - a r g (w) = \frac{π}{2}

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Sum of Infinite Terms

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