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Locating a Given Point on a Graph Paper

6.If Z1 , Z2 ...

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6.If Z1 , Z2 , Z3 are the vertices of an equilateral triangled such that |Z1| = |Z2| = |Z3| then prove that Z1+Z2+Z3 = 0.

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Q. If the complex numbers

z_{1}, z_{2}, z_{3}

represent the the vertices of an equilateral triangle such that

| z_{1} | = | z_{2} | = | z_{3} |

, then prove that

z_{1} + z_{2} + z_{3} = 0

Q. Let the complex numbers

z_{1}, z_{2}, z_{3}

represent the vertices of an equilateral triangle. Then prove that

\frac{1}{z_{1} - z_{2}} + \frac{1}{z_{2} - z_{3}} + \frac{1}{z_{3} - z_{1}} = 0

z_{1}, z_{2}, z_{3}

represent the vertices of an equilateral triangle such that

| z_{1} | = | z_{2} | = | z_{3} |

z_{1} + z_{2} + z_{3} = 0

| z_{1} | = | z_{2} | = | z_{2} | = 1

, then prove that the complex numbers

z_{1}, z_{2}, z_{3}

are the vertices of an equilateral triangle inscribed in the unit circle.

Q. If the complex numbers,

z_{1}, z_{2}, z_{3}

represent the vertices of an equilateral triangle such that

| z_{1} | = | z_{2} | = | z_{3} |,

z_{1} + z_{2} + z_{3} =

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