De Moivre's Theorem
« Previous Topic: Argand Plane and Polar Representation Next Topic: Solution of Quadratic and Higher Degree Equations »
NEET Test Series from KOTA - 10 Papers In MS WORD WhatsApp Here
Complex Numbers and Quadratic Equation

117996 If \(x_n=\cos \left(\frac{\pi}{4^n}\right)+i \sin \left(\frac{\pi}{4^n}\right)\), then \(x_1 \cdot x_2 \cdot x_3 \ldots \infty\) is

1 \(\frac{1+\mathrm{i} \sqrt{3}}{2}\)
2 \(\frac{-1+\mathrm{i} \sqrt{3}}{2}\)
3 \(\frac{1-\mathrm{i} \sqrt{3}}{2}\)
4 \(\frac{-1-\mathrm{i} \sqrt{3}}{2}\)
UPSEE-2012
Complex Numbers and Quadratic Equation

117997 \(\left(\frac{-1+\sqrt{-3}}{2}\right)^{100}+\left(\frac{-1-\sqrt{-3}}{2}\right)^{100}\) is equal to:

1 2
2 zero
3 -1
4 1
UPSEE-2005
Complex Numbers and Quadratic Equation

117998 If \(i=\sqrt{-1}\) and \(\left(\frac{1+1}{1-i}\right)^n=1\), then the least positive integral value of \(n\) is

1 2
2 4
3 1
4 3
JCECE-2019
Complex Numbers and Quadratic Equation

117999 \(\left[\frac{-1+\sqrt{(-3)}}{2}\right]^{3 \mathrm{n}}+\left[\frac{-1-\sqrt{(-3)}}{2}\right]^{3 \mathrm{n}}\) is equal to

1 0
2 1
3 2
4 3
CG PET- 2010
NEET DIGITAL LIBRARY
Complex Numbers and Quadratic Equation

117996 If \(x_n=\cos \left(\frac{\pi}{4^n}\right)+i \sin \left(\frac{\pi}{4^n}\right)\), then \(x_1 \cdot x_2 \cdot x_3 \ldots \infty\) is

1 \(\frac{1+\mathrm{i} \sqrt{3}}{2}\)
2 \(\frac{-1+\mathrm{i} \sqrt{3}}{2}\)
3 \(\frac{1-\mathrm{i} \sqrt{3}}{2}\)
4 \(\frac{-1-\mathrm{i} \sqrt{3}}{2}\)
UPSEE-2012
Complex Numbers and Quadratic Equation

117997 \(\left(\frac{-1+\sqrt{-3}}{2}\right)^{100}+\left(\frac{-1-\sqrt{-3}}{2}\right)^{100}\) is equal to:

1 2
2 zero
3 -1
4 1
UPSEE-2005
Complex Numbers and Quadratic Equation

117998 If \(i=\sqrt{-1}\) and \(\left(\frac{1+1}{1-i}\right)^n=1\), then the least positive integral value of \(n\) is

1 2
2 4
3 1
4 3
JCECE-2019
Complex Numbers and Quadratic Equation

117999 \(\left[\frac{-1+\sqrt{(-3)}}{2}\right]^{3 \mathrm{n}}+\left[\frac{-1-\sqrt{(-3)}}{2}\right]^{3 \mathrm{n}}\) is equal to

1 0
2 1
3 2
4 3
CG PET- 2010
Join With Us for More Updates
Complex Numbers and Quadratic Equation

117996 If \(x_n=\cos \left(\frac{\pi}{4^n}\right)+i \sin \left(\frac{\pi}{4^n}\right)\), then \(x_1 \cdot x_2 \cdot x_3 \ldots \infty\) is

1 \(\frac{1+\mathrm{i} \sqrt{3}}{2}\)
2 \(\frac{-1+\mathrm{i} \sqrt{3}}{2}\)
3 \(\frac{1-\mathrm{i} \sqrt{3}}{2}\)
4 \(\frac{-1-\mathrm{i} \sqrt{3}}{2}\)
UPSEE-2012
Complex Numbers and Quadratic Equation

117997 \(\left(\frac{-1+\sqrt{-3}}{2}\right)^{100}+\left(\frac{-1-\sqrt{-3}}{2}\right)^{100}\) is equal to:

1 2
2 zero
3 -1
4 1
UPSEE-2005
Complex Numbers and Quadratic Equation

117998 If \(i=\sqrt{-1}\) and \(\left(\frac{1+1}{1-i}\right)^n=1\), then the least positive integral value of \(n\) is

1 2
2 4
3 1
4 3
JCECE-2019
Complex Numbers and Quadratic Equation

117999 \(\left[\frac{-1+\sqrt{(-3)}}{2}\right]^{3 \mathrm{n}}+\left[\frac{-1-\sqrt{(-3)}}{2}\right]^{3 \mathrm{n}}\) is equal to

1 0
2 1
3 2
4 3
CG PET- 2010
For More Updates join with Us
NEET Test Series from KOTA - 10 Papers In MS WORD WhatsApp Here
Complex Numbers and Quadratic Equation

117996 If \(x_n=\cos \left(\frac{\pi}{4^n}\right)+i \sin \left(\frac{\pi}{4^n}\right)\), then \(x_1 \cdot x_2 \cdot x_3 \ldots \infty\) is

1 \(\frac{1+\mathrm{i} \sqrt{3}}{2}\)
2 \(\frac{-1+\mathrm{i} \sqrt{3}}{2}\)
3 \(\frac{1-\mathrm{i} \sqrt{3}}{2}\)
4 \(\frac{-1-\mathrm{i} \sqrt{3}}{2}\)
UPSEE-2012
Complex Numbers and Quadratic Equation

117997 \(\left(\frac{-1+\sqrt{-3}}{2}\right)^{100}+\left(\frac{-1-\sqrt{-3}}{2}\right)^{100}\) is equal to:

1 2
2 zero
3 -1
4 1
UPSEE-2005
Complex Numbers and Quadratic Equation

117998 If \(i=\sqrt{-1}\) and \(\left(\frac{1+1}{1-i}\right)^n=1\), then the least positive integral value of \(n\) is

1 2
2 4
3 1
4 3
JCECE-2019
Complex Numbers and Quadratic Equation

117999 \(\left[\frac{-1+\sqrt{(-3)}}{2}\right]^{3 \mathrm{n}}+\left[\frac{-1-\sqrt{(-3)}}{2}\right]^{3 \mathrm{n}}\) is equal to

1 0
2 1
3 2
4 3
CG PET- 2010
NEET DIGITAL LIBRARY