117985 If the four points \(A, B, C, D\) in the Argand plane represented respectively by the complex numbers \(2+i, 4+3 i, 2+5 i, 3 i\) lie on a circle, then the centre of the circle is

117986 If \(\left(\frac{\cos \theta+i \sin \theta}{\sin \theta+i \cos \theta}\right)^{2020}+\left(\frac{1+\cos \theta+i \sin \theta}{1-\cos \theta+i \sin \theta}\right)^{2021]}=x+\) iy, then the value of \(x+y\) at \(\theta=\frac{\pi}{2}\) is

117987 Let \(w=\frac{1-i z}{z-i}\). If \(|w|=1\), which of the following must be true?

117988 Let \(z_1=1+i \sqrt{3}\) and \(z_2=1+i\), then \(\arg \left(\frac{z_1}{z_2}\right)\) is

117985 If the four points \(A, B, C, D\) in the Argand plane represented respectively by the complex numbers \(2+i, 4+3 i, 2+5 i, 3 i\) lie on a circle, then the centre of the circle is

117986 If \(\left(\frac{\cos \theta+i \sin \theta}{\sin \theta+i \cos \theta}\right)^{2020}+\left(\frac{1+\cos \theta+i \sin \theta}{1-\cos \theta+i \sin \theta}\right)^{2021]}=x+\) iy, then the value of \(x+y\) at \(\theta=\frac{\pi}{2}\) is

117987 Let \(w=\frac{1-i z}{z-i}\). If \(|w|=1\), which of the following must be true?

117988 Let \(z_1=1+i \sqrt{3}\) and \(z_2=1+i\), then \(\arg \left(\frac{z_1}{z_2}\right)\) is

117985 If the four points \(A, B, C, D\) in the Argand plane represented respectively by the complex numbers \(2+i, 4+3 i, 2+5 i, 3 i\) lie on a circle, then the centre of the circle is

117986 If \(\left(\frac{\cos \theta+i \sin \theta}{\sin \theta+i \cos \theta}\right)^{2020}+\left(\frac{1+\cos \theta+i \sin \theta}{1-\cos \theta+i \sin \theta}\right)^{2021]}=x+\) iy, then the value of \(x+y\) at \(\theta=\frac{\pi}{2}\) is

117987 Let \(w=\frac{1-i z}{z-i}\). If \(|w|=1\), which of the following must be true?

117988 Let \(z_1=1+i \sqrt{3}\) and \(z_2=1+i\), then \(\arg \left(\frac{z_1}{z_2}\right)\) is

117985 If the four points \(A, B, C, D\) in the Argand plane represented respectively by the complex numbers \(2+i, 4+3 i, 2+5 i, 3 i\) lie on a circle, then the centre of the circle is

117986 If \(\left(\frac{\cos \theta+i \sin \theta}{\sin \theta+i \cos \theta}\right)^{2020}+\left(\frac{1+\cos \theta+i \sin \theta}{1-\cos \theta+i \sin \theta}\right)^{2021]}=x+\) iy, then the value of \(x+y\) at \(\theta=\frac{\pi}{2}\) is

117987 Let \(w=\frac{1-i z}{z-i}\). If \(|w|=1\), which of the following must be true?

117988 Let \(z_1=1+i \sqrt{3}\) and \(z_2=1+i\), then \(\arg \left(\frac{z_1}{z_2}\right)\) is