JEE MATHEMATICS MCQ: COMPLEX NUMBERS

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Analyzing +4 | -1

All the roots of the equation

a_1 z^3+a_2 z^2+a_3 z+a_4=3

, where

\left|a_j\right| \leq 1

i=1,2,3,4

, lie outside the circle with centre origin and radius

View answer and explanation

Correct option: C

\frac{1}{3}

Option C (

\frac{{1}}{{3}}

) is correct because all roots of the equation lie outside the circle with radius

\frac{{2}}{{3}}

, which means they lie outside the circle with radius

\frac{{1}}{{3}}

as well.

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

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z \neq \pm 1

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

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

a \neq 0

\alpha, \beta

\gamma

|\alpha-\beta|

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

z \in C

2x = - 1 + \sqrt 3 i

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