Let z be a imaginary number satisfying - z-1 - -1- Also -2z- -2- and -2- Then the value of - z - 2 - - 2 - - 2 - - 2 - z-2 - 2 - - -4 - 2 - - -8 - 2 - - -16 - 2- is-

In each of $α$ $β$ and $γ$ $is a positive acute angle such that$
$sin (α + β - γ) = \frac{1}{2}, cos (β + γ - α) = \frac{1}{2} and tan (γ + α - β) = 1$
Find the values of $α$ , $β$ , & $γ$ .

Q. If

0 < α, β, γ < \frac{π}{2}

such that

α + β + γ = \frac{π}{2}

and

cot α, cot β, cot γ

are in A.P., then the value of

cot α cot γ

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Let z be a imaginary number satisfying |z−1|=1. Also α=2z, β=2α and γ=2β. Then the value of |z|2+|α|2+|β|2+|γ|2+|z−2|2+|α−4|2+|β−8|2+|γ−16|2, is-

The correct option is B 340|z|2+|z−2|2=4Similarly |α|2+|α−4|2=16|β|2+|β−8|2=64|γ|2+|γ−16|2=256∴ Required sum =340

Let $z$ be a imaginary number satisfying $| z - 1 | = 1$ . Also $α = 2 z$ , $β = 2 α$ and $γ = 2 β$ . Then the value of ${| z |}^{2} + {| α |}^{2} + {| β |}^{2} + {| γ |}^{2} + {| z - 2 |}^{2} + {| α - 4 |}^{2} + {| β - 8 |}^{2} + {| γ - 16 |}^{2}$ , is-

The correct option is B $340$
${| z |}^{2} + {| z - 2 |}^{2} = 4$
Similarly
${| α |}^{2} + {| α - 4 |}^{2} = 16$
${| β |}^{2} + {| β - 8 |}^{2} = 64$
${| γ |}^{2} + {| γ - 16 |}^{2} = 256$
$∴$ Required sum $= 340$