If -1-4 i -2- x - - 5 where i -1 then x -A- RB- -2- -C- -4- -D- Z -

The correct option is B [ 2 ,∞ )|(1+4i) 2^ x |≤ 5⇒ |(1 2^ x )+4i| ≤ 5 Squaring on both sides ⇒ (1 2^ x )^2+16 ≤ 25⇒(1 2^ x )^9≤ 9 ⇒ 3 ≤ 1 2^ x≤ 3⇒ 4 ≤ 2^ x ...

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Standard XII

Mathematics

Local Maxima

If |1+4 i -2-...

Question

If $| 1 + 4 i - 2^{- x} | \leq 5$ where $i = \sqrt{- 1}$ then $x ϵ$

R

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[- 4, \infty)

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Z^{+}

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[- 2, \infty)

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Solution

The correct option is D $[- 2, \infty)$
$| (1 + 4 i) - 2^{- x} | \leq 5 \Rightarrow | (1 - 2^{- x}) + 4 i | \leq 5$
Squaring on both sides
$\Rightarrow (1 - 2^{- x})^{2} + 16 \leq 25 \Rightarrow (1 - 2^{- x})^{9} \leq 9$
$\Rightarrow - 3 \leq 1 - 2^{- x} \leq 3 \Rightarrow - 4 \leq - 2^{- x} \leq 2$
$\Rightarrow - 2 \leq 2^{- x} \leq 4$
$\Rightarrow 0 \leq 2^{- x} \leq 4 \Rightarrow 2^{- \infty} \leq 2^{- x} \leq 2^{2}$
$\Rightarrow x ϵ [- 2, \infty)$

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If |1+4i−2−x|≤5 where i=√−1 then xϵ

The correct option is D [−2,∞)|(1+4i)−2−x|≤5⇒|(1−2−x)+4i|≤5 Squaring on both sides ⇒(1−2−x)2+16≤25⇒(1−2−x)9≤9 ⇒−3≤1−2−x≤3⇒−4≤−2−x≤2 ⇒−2≤2−x≤4 ⇒0≤2−x≤4⇒2−∞≤2−x≤22 ⇒xϵ[−2,∞)

If $| 1 + 4 i - 2^{- x} | \leq 5$ where $i = \sqrt{- 1}$ then $x ϵ$