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Quadrilaterals

If |z|+2=I(z)...

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If |z|+2=I(z), then z= (x,y) lies on-

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z = x + i y

ω = \frac{1 - i z}{z - i}

| ω | = 1

z

∣ ∣ z + ¯ ¯ ¯ z ∣ ∣ + ∣ ∣ z - ¯ ¯ ¯ z ∣ ∣ = 2

, then z lies on

z = x + i y a n d w = \frac{1 - i z}{z - i},

| w | = 1

implies that, on the complex plane

If $z = x + i y$ and $ω = \frac{1 - i z}{z - i}$ , then $| ω | = 1$ implies that, in the complex plane $z$ lies on the real axis.

Q. If the point (x, y, z) lies on the plane x + y + z = 3 then

x^{2} + y^{2} + z^{2} ⩾ 3

. Prove this fact.

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