117821 If \(\alpha\) and \(\beta\) are different complex numbers with \(|\beta|=1\), then \(\left|\frac{\beta-\alpha}{1-\bar{\alpha} \beta}\right|\) is equal to

117822 If \(z\) is complex number of unit modulus and argument \(\theta\),then \(\arg \left(\frac{1+z}{1+\bar{z}}\right)\) equals

117824 The modulus of \([1-\cos \theta+i \sin \theta]^{-1}\) is

117825 If \(\left|\mathbf{z}_1\right|=\left|z_2\right|=\ldots \ldots .\left|z_n\right|=1\), then the value of \(\left|\mathrm{z}_1+\mathrm{z}_2+\ldots \ldots . \mathrm{z}_{\mathrm{n}}\right|-\left|\frac{\mathbf{1}}{\mathrm{z}_1}+\frac{\mathbf{1}}{\mathrm{z}_2}+\ldots \ldots .+\frac{\mathbf{1}}{\mathbf{z}_{\mathrm{n}}}\right|\) is,

117826 The modulus of the complex number \(z\) such that \(|z+3-i|=1\) and \(\arg (z)=\pi\) is equal to

117821 If \(\alpha\) and \(\beta\) are different complex numbers with \(|\beta|=1\), then \(\left|\frac{\beta-\alpha}{1-\bar{\alpha} \beta}\right|\) is equal to

117822 If \(z\) is complex number of unit modulus and argument \(\theta\),then \(\arg \left(\frac{1+z}{1+\bar{z}}\right)\) equals

117824 The modulus of \([1-\cos \theta+i \sin \theta]^{-1}\) is

117825 If \(\left|\mathbf{z}_1\right|=\left|z_2\right|=\ldots \ldots .\left|z_n\right|=1\), then the value of \(\left|\mathrm{z}_1+\mathrm{z}_2+\ldots \ldots . \mathrm{z}_{\mathrm{n}}\right|-\left|\frac{\mathbf{1}}{\mathrm{z}_1}+\frac{\mathbf{1}}{\mathrm{z}_2}+\ldots \ldots .+\frac{\mathbf{1}}{\mathbf{z}_{\mathrm{n}}}\right|\) is,

117826 The modulus of the complex number \(z\) such that \(|z+3-i|=1\) and \(\arg (z)=\pi\) is equal to

117821 If \(\alpha\) and \(\beta\) are different complex numbers with \(|\beta|=1\), then \(\left|\frac{\beta-\alpha}{1-\bar{\alpha} \beta}\right|\) is equal to

117822 If \(z\) is complex number of unit modulus and argument \(\theta\),then \(\arg \left(\frac{1+z}{1+\bar{z}}\right)\) equals

117824 The modulus of \([1-\cos \theta+i \sin \theta]^{-1}\) is

117825 If \(\left|\mathbf{z}_1\right|=\left|z_2\right|=\ldots \ldots .\left|z_n\right|=1\), then the value of \(\left|\mathrm{z}_1+\mathrm{z}_2+\ldots \ldots . \mathrm{z}_{\mathrm{n}}\right|-\left|\frac{\mathbf{1}}{\mathrm{z}_1}+\frac{\mathbf{1}}{\mathrm{z}_2}+\ldots \ldots .+\frac{\mathbf{1}}{\mathbf{z}_{\mathrm{n}}}\right|\) is,

117826 The modulus of the complex number \(z\) such that \(|z+3-i|=1\) and \(\arg (z)=\pi\) is equal to

117821 If \(\alpha\) and \(\beta\) are different complex numbers with \(|\beta|=1\), then \(\left|\frac{\beta-\alpha}{1-\bar{\alpha} \beta}\right|\) is equal to

117822 If \(z\) is complex number of unit modulus and argument \(\theta\),then \(\arg \left(\frac{1+z}{1+\bar{z}}\right)\) equals

117824 The modulus of \([1-\cos \theta+i \sin \theta]^{-1}\) is

117825 If \(\left|\mathbf{z}_1\right|=\left|z_2\right|=\ldots \ldots .\left|z_n\right|=1\), then the value of \(\left|\mathrm{z}_1+\mathrm{z}_2+\ldots \ldots . \mathrm{z}_{\mathrm{n}}\right|-\left|\frac{\mathbf{1}}{\mathrm{z}_1}+\frac{\mathbf{1}}{\mathrm{z}_2}+\ldots \ldots .+\frac{\mathbf{1}}{\mathbf{z}_{\mathrm{n}}}\right|\) is,

117826 The modulus of the complex number \(z\) such that \(|z+3-i|=1\) and \(\arg (z)=\pi\) is equal to

117821 If \(\alpha\) and \(\beta\) are different complex numbers with \(|\beta|=1\), then \(\left|\frac{\beta-\alpha}{1-\bar{\alpha} \beta}\right|\) is equal to

117822 If \(z\) is complex number of unit modulus and argument \(\theta\),then \(\arg \left(\frac{1+z}{1+\bar{z}}\right)\) equals

117824 The modulus of \([1-\cos \theta+i \sin \theta]^{-1}\) is

117825 If \(\left|\mathbf{z}_1\right|=\left|z_2\right|=\ldots \ldots .\left|z_n\right|=1\), then the value of \(\left|\mathrm{z}_1+\mathrm{z}_2+\ldots \ldots . \mathrm{z}_{\mathrm{n}}\right|-\left|\frac{\mathbf{1}}{\mathrm{z}_1}+\frac{\mathbf{1}}{\mathrm{z}_2}+\ldots \ldots .+\frac{\mathbf{1}}{\mathbf{z}_{\mathrm{n}}}\right|\) is,

117826 The modulus of the complex number \(z\) such that \(|z+3-i|=1\) and \(\arg (z)=\pi\) is equal to