(D) Given the inequality $|z|^2 - |z| - 2 0$,so $t -

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(D) Given the inequality $|z|^2 - |z| - 2 Let $t = |z|$,then $t^2 - t - 2 $(t - 2)(t + 1) Since $|z| \ge 0$,we have $t + 1 > 0$,so $t - 2 Now,using the triangle inequality $|a + b| \le |a| + |b|$,we have:$|z^2 + z \sin \theta| \le |z^2| + |z \sin \theta| = |z|^2 + |z| \cdot |\sin \theta|$.Since $|\sin \theta| \le 1$,we get $|z^2 + z \sin \theta| \le |z|^2 + |z|$.Since $|z| Therefore,$|z|^2 + |z| Thus,$|z^2 + z \sin \theta| < 6$.

Class 11 Mathematics 4-1.Complex numbers Mix Examples-Complex numbers

If $z$ is a complex number satisfying $|z|^2 - |z| - 2 < 0$,then the value of $|z^2 + z \sin \theta|$,for all values of $\theta$,is

A
equal to $4$
B
equal to $6$
C
more than $6$
D
less than $6$

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4-1.Complex numbers

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Mix Examples-Complex numbers

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The number of solutions for $z^3+\bar{z}=0$ is

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If the complex numbers $z_1, z_2$ and the origin form an equilateral triangle,then $z_1^2 + z_2^2 = $

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If $z$ is a complex number satisfying $|z|^2 - |z| - 2 < 0$,then the value of $|z^2 + z \sin \theta|$,for all values of $\theta$,is

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