Suppose z is any root of 11 z^8 + 21 i z^7 + | vedclass

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(B) Given the equation $11 z^8 + 21 i z^7 + 10 i z - 22 = 0$.We can rewrite this as $11 z^8 - 22 = -21 i z^7 - 10 i z$.Taking the modulus on both side

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$3 < S < 7$

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(B) Given the equation $11 z^8 + 21 i z^7 + 10 i z - 22 = 0$.We can rewrite this as $11 z^8 - 22 = -21 i z^7 - 10 i z$.Taking the modulus on both sides,we get $|11 z^8 - 22| = |-21 i z^7 - 10 i z|$.Using the triangle inequality,$|11 z^8 - 22| \leq |11 z^8| + |-22| = 11|z|^8 + 22$.Also,$|-21 i z^7 - 10 i z| = |21 i z^7 + 10 i z| = |z| |21 i z^6 + 10 i| \leq |z| (21|z|^6 + 10)$.By Rouché's theorem or analyzing the bounds of the roots,it can be shown that for this polynomial,the roots satisfy $1 Let $r = |z|$. Then $1 We define $S = r^2 + r + 1$.Since $1 This simplifies to $3 Thus,the correct option is $B$.

Suppose $z$ is any root of $11 z^8 + 21 i z^7 + 10 i z - 22 = 0$ where $i = \sqrt{-1}$. Then,$S = |z|^2 + |z| + 1$ satisfies

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