Argand Plane and Polar Representation
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Complex Numbers and Quadratic Equation

117966 If \(z_1=\sqrt{3}-i\) and \(z_2=1+i \sqrt{3}\), then \(\operatorname{amp}\left(\mathrm{z}_1+\mathrm{z}_2\right)=\)

1 \(\frac{\pi}{12}\)
2 \(\frac{\pi}{15}\)
3 \(\frac{\pi}{6}\)
4 \(\frac{\pi}{4}\)
COMEDK-2011
Complex Numbers and Quadratic Equation

117958 If \(z(2-i)=3+i, z^{20}=\)

1 \(1-i\)
2 -1024
3 1024
4 \(1+i\)
Karnataka CET-2002
Complex Numbers and Quadratic Equation

117959 If \(z=r^{i \theta}\) then \(\left|e^{i z}\right|\) is equal to

1 \(\mathrm{e}^{-\mathrm{rsin} \theta}\)
2 \(\mathrm{re}^{-\mathrm{r} \sin \theta}\)
3 \(\mathrm{e}^{-\mathrm{r} \cos \theta}\)
4 \(\mathrm{re}^{-\mathrm{r} \cos \theta}\)
Kerala CEE - 2005]
Complex Numbers and Quadratic Equation

117960 The region of the argand diagram defined by \(|\mathbf{z}-\mathbf{1}|+|\mathbf{z}+\mathbf{1}| \leq 4\) is

1 Interior of an ellipse
2 exterior of a circle
3 interior and bondry of an ellipse
4 interior of a circle
SRM JEEE-2011
Complex Numbers and Quadratic Equation

117961 The real part of \((1-\cos \theta+i \sin \theta)^{-1}\) is

1 \(\frac{1}{2}\)
2 \(\frac{1}{1+\cos \theta}\)
3 \(\tan \frac{\theta}{2}\)
4 \(\cot \frac{\theta}{2}\)
Karnataka CET-2016
NEET DIGITAL LIBRARY
Complex Numbers and Quadratic Equation

117966 If \(z_1=\sqrt{3}-i\) and \(z_2=1+i \sqrt{3}\), then \(\operatorname{amp}\left(\mathrm{z}_1+\mathrm{z}_2\right)=\)

1 \(\frac{\pi}{12}\)
2 \(\frac{\pi}{15}\)
3 \(\frac{\pi}{6}\)
4 \(\frac{\pi}{4}\)
COMEDK-2011
Complex Numbers and Quadratic Equation

117958 If \(z(2-i)=3+i, z^{20}=\)

1 \(1-i\)
2 -1024
3 1024
4 \(1+i\)
Karnataka CET-2002
Complex Numbers and Quadratic Equation

117959 If \(z=r^{i \theta}\) then \(\left|e^{i z}\right|\) is equal to

1 \(\mathrm{e}^{-\mathrm{rsin} \theta}\)
2 \(\mathrm{re}^{-\mathrm{r} \sin \theta}\)
3 \(\mathrm{e}^{-\mathrm{r} \cos \theta}\)
4 \(\mathrm{re}^{-\mathrm{r} \cos \theta}\)
Kerala CEE - 2005]
Complex Numbers and Quadratic Equation

117960 The region of the argand diagram defined by \(|\mathbf{z}-\mathbf{1}|+|\mathbf{z}+\mathbf{1}| \leq 4\) is

1 Interior of an ellipse
2 exterior of a circle
3 interior and bondry of an ellipse
4 interior of a circle
SRM JEEE-2011
Complex Numbers and Quadratic Equation

117961 The real part of \((1-\cos \theta+i \sin \theta)^{-1}\) is

1 \(\frac{1}{2}\)
2 \(\frac{1}{1+\cos \theta}\)
3 \(\tan \frac{\theta}{2}\)
4 \(\cot \frac{\theta}{2}\)
Karnataka CET-2016
Join With Us for More Updates
Complex Numbers and Quadratic Equation

117966 If \(z_1=\sqrt{3}-i\) and \(z_2=1+i \sqrt{3}\), then \(\operatorname{amp}\left(\mathrm{z}_1+\mathrm{z}_2\right)=\)

1 \(\frac{\pi}{12}\)
2 \(\frac{\pi}{15}\)
3 \(\frac{\pi}{6}\)
4 \(\frac{\pi}{4}\)
COMEDK-2011
Complex Numbers and Quadratic Equation

117958 If \(z(2-i)=3+i, z^{20}=\)

1 \(1-i\)
2 -1024
3 1024
4 \(1+i\)
Karnataka CET-2002
Complex Numbers and Quadratic Equation

117959 If \(z=r^{i \theta}\) then \(\left|e^{i z}\right|\) is equal to

1 \(\mathrm{e}^{-\mathrm{rsin} \theta}\)
2 \(\mathrm{re}^{-\mathrm{r} \sin \theta}\)
3 \(\mathrm{e}^{-\mathrm{r} \cos \theta}\)
4 \(\mathrm{re}^{-\mathrm{r} \cos \theta}\)
Kerala CEE - 2005]
Complex Numbers and Quadratic Equation

117960 The region of the argand diagram defined by \(|\mathbf{z}-\mathbf{1}|+|\mathbf{z}+\mathbf{1}| \leq 4\) is

1 Interior of an ellipse
2 exterior of a circle
3 interior and bondry of an ellipse
4 interior of a circle
SRM JEEE-2011
Complex Numbers and Quadratic Equation

117961 The real part of \((1-\cos \theta+i \sin \theta)^{-1}\) is

1 \(\frac{1}{2}\)
2 \(\frac{1}{1+\cos \theta}\)
3 \(\tan \frac{\theta}{2}\)
4 \(\cot \frac{\theta}{2}\)
Karnataka CET-2016
For More Updates join with Us
Complex Numbers and Quadratic Equation

117966 If \(z_1=\sqrt{3}-i\) and \(z_2=1+i \sqrt{3}\), then \(\operatorname{amp}\left(\mathrm{z}_1+\mathrm{z}_2\right)=\)

1 \(\frac{\pi}{12}\)
2 \(\frac{\pi}{15}\)
3 \(\frac{\pi}{6}\)
4 \(\frac{\pi}{4}\)
COMEDK-2011
Complex Numbers and Quadratic Equation

117958 If \(z(2-i)=3+i, z^{20}=\)

1 \(1-i\)
2 -1024
3 1024
4 \(1+i\)
Karnataka CET-2002
Complex Numbers and Quadratic Equation

117959 If \(z=r^{i \theta}\) then \(\left|e^{i z}\right|\) is equal to

1 \(\mathrm{e}^{-\mathrm{rsin} \theta}\)
2 \(\mathrm{re}^{-\mathrm{r} \sin \theta}\)
3 \(\mathrm{e}^{-\mathrm{r} \cos \theta}\)
4 \(\mathrm{re}^{-\mathrm{r} \cos \theta}\)
Kerala CEE - 2005]
Complex Numbers and Quadratic Equation

117960 The region of the argand diagram defined by \(|\mathbf{z}-\mathbf{1}|+|\mathbf{z}+\mathbf{1}| \leq 4\) is

1 Interior of an ellipse
2 exterior of a circle
3 interior and bondry of an ellipse
4 interior of a circle
SRM JEEE-2011
Complex Numbers and Quadratic Equation

117961 The real part of \((1-\cos \theta+i \sin \theta)^{-1}\) is

1 \(\frac{1}{2}\)
2 \(\frac{1}{1+\cos \theta}\)
3 \(\tan \frac{\theta}{2}\)
4 \(\cot \frac{\theta}{2}\)
Karnataka CET-2016
NEET DIGITAL LIBRARY
Complex Numbers and Quadratic Equation

117966 If \(z_1=\sqrt{3}-i\) and \(z_2=1+i \sqrt{3}\), then \(\operatorname{amp}\left(\mathrm{z}_1+\mathrm{z}_2\right)=\)

1 \(\frac{\pi}{12}\)
2 \(\frac{\pi}{15}\)
3 \(\frac{\pi}{6}\)
4 \(\frac{\pi}{4}\)
COMEDK-2011
Complex Numbers and Quadratic Equation

117958 If \(z(2-i)=3+i, z^{20}=\)

1 \(1-i\)
2 -1024
3 1024
4 \(1+i\)
Karnataka CET-2002
Complex Numbers and Quadratic Equation

117959 If \(z=r^{i \theta}\) then \(\left|e^{i z}\right|\) is equal to

1 \(\mathrm{e}^{-\mathrm{rsin} \theta}\)
2 \(\mathrm{re}^{-\mathrm{r} \sin \theta}\)
3 \(\mathrm{e}^{-\mathrm{r} \cos \theta}\)
4 \(\mathrm{re}^{-\mathrm{r} \cos \theta}\)
Kerala CEE - 2005]
Complex Numbers and Quadratic Equation

117960 The region of the argand diagram defined by \(|\mathbf{z}-\mathbf{1}|+|\mathbf{z}+\mathbf{1}| \leq 4\) is

1 Interior of an ellipse
2 exterior of a circle
3 interior and bondry of an ellipse
4 interior of a circle
SRM JEEE-2011
Complex Numbers and Quadratic Equation

117961 The real part of \((1-\cos \theta+i \sin \theta)^{-1}\) is

1 \(\frac{1}{2}\)
2 \(\frac{1}{1+\cos \theta}\)
3 \(\tan \frac{\theta}{2}\)
4 \(\cot \frac{\theta}{2}\)
Karnataka CET-2016