If x + frac{1}{x} = 2cos θ , then x is equal to

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4-1.Complex numbers

easy

If $x + \frac{1}{x} = 2\cos \theta ,$ then $x$ is equal to

$\cos \theta + i\,\sin \theta $

$\cos \theta - i\,\sin \theta $

$\cos \theta \pm i\,\sin \theta $

$\sin \theta \pm i\,\cos \theta $

Solution

(c) $x + \frac{1}{x} = 2\cos \theta $$ \Rightarrow \,{x^2} – 2x\cos \theta + 1 = 0$
==> $x = \frac{{2\cos \theta \pm \sqrt {4{{\cos }^2}\theta – 4} }}{2}$ ==> $x = \cos \theta \pm i\sin \theta $.

Standard 11

Mathematics

Let $z$ be a complex number such that the imaginary part of $z$ is non zero and $a=z^2+z+1$ is real. Then a cannot take the value

hard

(IIT-2012)

If $z \neq 0$ be a complex number such that $\left| z -\frac{1}{ z }\right|=2$, then the maximum value of $|z|$ is.

hard

(JEE MAIN-2022)

The value of $\frac{{{i^{592}} + {i^{590}} + {i^{588}} + {i^{586}} + {i^{584}}}}{{{i^{582}} + {i^{580}} + {i^{578}} + {i^{576}} + {i^{574}}}} – 1 = $

medium

If the real part of the complex number $z=\frac{3+2 i \cos \theta}{1-3 i \cos \theta}, \theta \in\left(0, \frac{\pi}{2}\right)$ is zero, then the value of $\sin ^{2} 3 \theta+\cos ^{2} \theta$ is equal to $…..$

medium

(JEE MAIN-2021)

Solve the equation $27 x^{2}-10 x+1=0$

medium

If $x + \frac{1}{x} = 2\cos \theta ,$ then $x$ is equal to

Solution

Similar Questions

Let $z$ be a complex number such that the imaginary part of $z$ is non zero and $a=z^2+z+1$ is real. Then a cannot take the value

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