JEE MATHEMATICS MCQ: COMPLEX NUMBERS

1 Easy

1 of 1

Application +4 | -1

Let

\left(-2-\frac{1}{3} \mathrm{i}\right)^3=\frac{\mathrm{x}+\mathrm{iy}}{27}(\mathrm{i}=\sqrt{-1})

, where

\mathrm{x}

and

y

are real numbers, then

y-x

equals :

View answer and explanation

Correct option: D

Option D (91) is correct because expanding the complex number expression and then calculating y - x results in 91.

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{\left| {1 - i} \right|^x} = {2^x}

|z|=1

z \neq \pm 1

z, \frac{z}{1-z^2}

\left|z_r-r\right| \leq r, \forall r=1,2,3, \ldots, n

\left|\sum\limits_{r=1}^n z_r\right|

(z+a b)^3=a^3

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\alpha, \beta

\gamma

|\alpha-\beta|

{z^2} + {\left| z \right|^2} = 0,

z \in C

2x = - 1 + \sqrt 3 i

{\left( {1 - {x^2} + x} \right)^6} - {\left( {1 - x + {x^2}} \right)^6}