State true or false- z1-z2-z3-A-z1-z2- -z3- 2-B- z1-z2- 2-z3- -C- then A-B-C-3 z1-Type 0 for false and 1 for true

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Summation by Sigma Method

State true or...

Question

State true or false:

$z_{1} + z_{2} + z_{3} = A, z_{1} + z_{2} ω + z_{3} ω^{2} = B,$ $z_{1} + z_{2} ω^{2} + z_{3} ω = C .$ then $A + B + C = 3 z_{1}$ .
Type 0 for false and 1 for true

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A = Z_{1} + Z_{2} + Z_{3}, B = Z_{1} + Z_{2} ω + Z_{3} ω^{2}, C = Z_{1} + Z_{2} ω^{2} + Z_{3} ω

Z_{1}, Z_{2}, Z_{3}

A, B, C

z_{1} + z_{2} + z_{3} = A, z_{1} + z_{2} ω + z_{3} ω^{2} = B, z_{1} + z_{2} ω^{3} + z_{3} ω = C

| A |^{2} + | B |^{2} + | C |^{2} = 3 (| z_{1} |^{2} + | z_{2} |^{2} + | z_{3} |^{2})

z_{1} + z_{2} + z_{3} = A, z_{1} + z_{2} ω + z_{3} ω^{2} = B, z_{1} + z_{2} ω^{3} + z_{3} ω = C

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

z_{1} + z_{2} + z_{3} = A, z_{1} + z_{2} ω + z_{3} ω^{2} = B, z_{1} + z_{2} ω^{2} + z_{3} ω = C

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

A, B, C, ω

z_{1} = 1 + 2 i, z_{2} = 2 + 3 i, z_{3} = 3 + 4 i,

z_{1}, z_{2}

z_{3}

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