(A) Suppose there exists a complex number $z$ such that $z^4 + z + 2 = 0$ and $|z| < 1$.Then $z^4 + z = -2$.Taking the modulus on both sides,we get $|

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(A) Suppose there exists a complex number $z$ such that $z^4 + z + 2 = 0$ and $|z| Then $z^4 + z = -2$.Taking the modulus on both sides,we get $|z^4 + z| = |-2| = 2$.By the triangle inequality,$|z^4 + z| \le |z^4| + |z| = |z|^4 + |z|$.Since $|z| Therefore,$|z^4 + z| This implies $2 Thus,the equation cannot have a root such that $|z| < 1$.

Class 11 Mathematics 1 Complex Numbers and Quadratic Equations: Complex Numbers Conjugate and Modulus of complex numbers

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Let $z$ be a complex number. Then the equation $z^4 + z + 2 = 0$ cannot have a root such that:

A
$|z| < 1$
B
$|z| = 1$
C
$|z| > 1$
D
None of these

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1 Complex Numbers and Quadratic Equations: Complex Numbers

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Conjugate and Modulus of complex numbers

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Let $z$ be a complex number. Then the equation $z^4 + z + 2 = 0$ cannot have a root such that:

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If $|z_1| = |z_2| = \dots = |z_n| = 1$,then the value of $|z_1 + z_2 + z_3 + \dots + z_n|$ is equal to:

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