-3-356i3 is an integer where i-1- The value of the integer is equal to-

The correct option is B 24 →( √( 3 ) + 3 ^ 56 i ) #160; ^ 3 =3( 1+√( 3 ) i ) #160; ^ 3 =3( 1+√( 3 ) i ) #160; ^ 2 ( 1+√( 3 ) i ) → 3( 1+√ ...

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Byju's Answer

Standard XII

Mathematics

Properties of Iota

√3+356i3 is a...

Question

${⎛ ⎜ ⎝ \sqrt[3]{3} + ⎛ ⎜ ⎝ 3^{\frac{5}{6}} ⎞ ⎟ ⎠ i ⎞ ⎟ ⎠}^{3}$ is an integer where $i = \sqrt{- 1}$ . The value of the integer is equal to.

24

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Solution

The correct option is B $- 24$
$\to {⎛ ⎜ ⎝ \sqrt[3]{3} + 3^{\frac{5}{6}} i ⎞ ⎟ ⎠}^{3} = 3 {(1 + \sqrt{3} i)}^{3} = 3 {(1 + \sqrt{3} i)}^{2} (1 + \sqrt{3} i)$
$\to 3 {(1 + \sqrt{3} i)}^{3} = 3 (1 + 3 \sqrt{3} i^{3} + 3 \sqrt{3} i (1 + \sqrt{3} i))$
$\to 3 (1 - 3 \sqrt{3} i + 3 \sqrt{3} i - 9)$
$\to 3 (- 8) = - 24$

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⎛⎜⎝3√3+⎛⎜⎝356⎞⎟⎠i⎞⎟⎠3 is an integer where i=√−1. The value of the integer is equal to.

The correct option is B −24→⎛⎜⎝3√3+356i⎞⎟⎠3=3(1+√3i)3=3(1+√3i)2(1+√3i)→3(1+√3i)3=3(1+3√3i3+3√3i(1+√3i))→3(1−3√3i+3√3i−9)→3(−8)=−24

${⎛ ⎜ ⎝ \sqrt[3]{3} + ⎛ ⎜ ⎝ 3^{\frac{5}{6}} ⎞ ⎟ ⎠ i ⎞ ⎟ ⎠}^{3}$ is an integer where $i = \sqrt{- 1}$ . The value of the integer is equal to.