Concepts of Complex Numbers
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Complex Numbers and Quadratic Equation

117480 If \(\frac{3}{2+\cos \theta+i \sin \theta}=a+i b\) then \(\left[(a-b)^2+b^2\right]\) is equal to

1 0
2 1
3 -1
4 2
BCECE-2009
Complex Numbers and Quadratic Equation

117483 The real value of \(\alpha\) for which the expression \(\frac{1-i \sin \alpha}{1+2 i \sin \alpha}\) is purely real, is :

1 \((2 n+1) \frac{\pi}{2}\)
2 \((\mathrm{n}+1) \frac{\pi}{2}\)
3 \(\mathrm{n} \pi\)
4 none of these
BCECE-2005
Complex Numbers and Quadratic Equation

117484 If the imaginary part of \(\frac{2 z+1}{i z+1}\) is -2 , then the locus of the point represented by \(z\) is a:

1 circle
2 straight line
3 parabola
4 none of these
BCECE-2004
Complex Numbers and Quadratic Equation

117485 The values of \(x\) and \(y\) satisfying the equation
\(\frac{(1+\mathbf{i}) \mathbf{x}-\mathbf{2}}{3+\mathbf{i}}+\frac{(2-3 \mathbf{i}) \mathbf{y}+\mathbf{i}}{3-\mathbf{i}}=\mathbf{i} \text { are : }\)

1 \(x=-1, x=3\)
2 \(x=3, y=-1\)
3 \(x=0, y=1\)
4 \(\mathrm{x}=1, \mathrm{y}=0\)
BCECE-2003
Complex Numbers and Quadratic Equation

117486 The number of solutions of equation \(\mathrm{z}^2+\overline{\mathrm{z}}=0\), where \(\mathrm{z} \in \mathrm{C}\) are

1 6
2 1
3 4
4 5
Karnataka CET-2012
Join With Us for More Updates
Complex Numbers and Quadratic Equation

117480 If \(\frac{3}{2+\cos \theta+i \sin \theta}=a+i b\) then \(\left[(a-b)^2+b^2\right]\) is equal to

1 0
2 1
3 -1
4 2
BCECE-2009
Complex Numbers and Quadratic Equation

117483 The real value of \(\alpha\) for which the expression \(\frac{1-i \sin \alpha}{1+2 i \sin \alpha}\) is purely real, is :

1 \((2 n+1) \frac{\pi}{2}\)
2 \((\mathrm{n}+1) \frac{\pi}{2}\)
3 \(\mathrm{n} \pi\)
4 none of these
BCECE-2005
Complex Numbers and Quadratic Equation

117484 If the imaginary part of \(\frac{2 z+1}{i z+1}\) is -2 , then the locus of the point represented by \(z\) is a:

1 circle
2 straight line
3 parabola
4 none of these
BCECE-2004
Complex Numbers and Quadratic Equation

117485 The values of \(x\) and \(y\) satisfying the equation
\(\frac{(1+\mathbf{i}) \mathbf{x}-\mathbf{2}}{3+\mathbf{i}}+\frac{(2-3 \mathbf{i}) \mathbf{y}+\mathbf{i}}{3-\mathbf{i}}=\mathbf{i} \text { are : }\)

1 \(x=-1, x=3\)
2 \(x=3, y=-1\)
3 \(x=0, y=1\)
4 \(\mathrm{x}=1, \mathrm{y}=0\)
BCECE-2003
Complex Numbers and Quadratic Equation

117486 The number of solutions of equation \(\mathrm{z}^2+\overline{\mathrm{z}}=0\), where \(\mathrm{z} \in \mathrm{C}\) are

1 6
2 1
3 4
4 5
Karnataka CET-2012
For More Updates join with Us
NEET Test Series from KOTA - 10 Papers In MS WORD WhatsApp Here
Complex Numbers and Quadratic Equation

117480 If \(\frac{3}{2+\cos \theta+i \sin \theta}=a+i b\) then \(\left[(a-b)^2+b^2\right]\) is equal to

1 0
2 1
3 -1
4 2
BCECE-2009
Complex Numbers and Quadratic Equation

117483 The real value of \(\alpha\) for which the expression \(\frac{1-i \sin \alpha}{1+2 i \sin \alpha}\) is purely real, is :

1 \((2 n+1) \frac{\pi}{2}\)
2 \((\mathrm{n}+1) \frac{\pi}{2}\)
3 \(\mathrm{n} \pi\)
4 none of these
BCECE-2005
Complex Numbers and Quadratic Equation

117484 If the imaginary part of \(\frac{2 z+1}{i z+1}\) is -2 , then the locus of the point represented by \(z\) is a:

1 circle
2 straight line
3 parabola
4 none of these
BCECE-2004
Complex Numbers and Quadratic Equation

117485 The values of \(x\) and \(y\) satisfying the equation
\(\frac{(1+\mathbf{i}) \mathbf{x}-\mathbf{2}}{3+\mathbf{i}}+\frac{(2-3 \mathbf{i}) \mathbf{y}+\mathbf{i}}{3-\mathbf{i}}=\mathbf{i} \text { are : }\)

1 \(x=-1, x=3\)
2 \(x=3, y=-1\)
3 \(x=0, y=1\)
4 \(\mathrm{x}=1, \mathrm{y}=0\)
BCECE-2003
Complex Numbers and Quadratic Equation

117486 The number of solutions of equation \(\mathrm{z}^2+\overline{\mathrm{z}}=0\), where \(\mathrm{z} \in \mathrm{C}\) are

1 6
2 1
3 4
4 5
Karnataka CET-2012
NEET DIGITAL LIBRARY
Complex Numbers and Quadratic Equation

117480 If \(\frac{3}{2+\cos \theta+i \sin \theta}=a+i b\) then \(\left[(a-b)^2+b^2\right]\) is equal to

1 0
2 1
3 -1
4 2
BCECE-2009
Complex Numbers and Quadratic Equation

117483 The real value of \(\alpha\) for which the expression \(\frac{1-i \sin \alpha}{1+2 i \sin \alpha}\) is purely real, is :

1 \((2 n+1) \frac{\pi}{2}\)
2 \((\mathrm{n}+1) \frac{\pi}{2}\)
3 \(\mathrm{n} \pi\)
4 none of these
BCECE-2005
Complex Numbers and Quadratic Equation

117484 If the imaginary part of \(\frac{2 z+1}{i z+1}\) is -2 , then the locus of the point represented by \(z\) is a:

1 circle
2 straight line
3 parabola
4 none of these
BCECE-2004
Complex Numbers and Quadratic Equation

117485 The values of \(x\) and \(y\) satisfying the equation
\(\frac{(1+\mathbf{i}) \mathbf{x}-\mathbf{2}}{3+\mathbf{i}}+\frac{(2-3 \mathbf{i}) \mathbf{y}+\mathbf{i}}{3-\mathbf{i}}=\mathbf{i} \text { are : }\)

1 \(x=-1, x=3\)
2 \(x=3, y=-1\)
3 \(x=0, y=1\)
4 \(\mathrm{x}=1, \mathrm{y}=0\)
BCECE-2003
Complex Numbers and Quadratic Equation

117486 The number of solutions of equation \(\mathrm{z}^2+\overline{\mathrm{z}}=0\), where \(\mathrm{z} \in \mathrm{C}\) are

1 6
2 1
3 4
4 5
Karnataka CET-2012
Join With Us for More Updates
Complex Numbers and Quadratic Equation

117480 If \(\frac{3}{2+\cos \theta+i \sin \theta}=a+i b\) then \(\left[(a-b)^2+b^2\right]\) is equal to

1 0
2 1
3 -1
4 2
BCECE-2009
Complex Numbers and Quadratic Equation

117483 The real value of \(\alpha\) for which the expression \(\frac{1-i \sin \alpha}{1+2 i \sin \alpha}\) is purely real, is :

1 \((2 n+1) \frac{\pi}{2}\)
2 \((\mathrm{n}+1) \frac{\pi}{2}\)
3 \(\mathrm{n} \pi\)
4 none of these
BCECE-2005
Complex Numbers and Quadratic Equation

117484 If the imaginary part of \(\frac{2 z+1}{i z+1}\) is -2 , then the locus of the point represented by \(z\) is a:

1 circle
2 straight line
3 parabola
4 none of these
BCECE-2004
Complex Numbers and Quadratic Equation

117485 The values of \(x\) and \(y\) satisfying the equation
\(\frac{(1+\mathbf{i}) \mathbf{x}-\mathbf{2}}{3+\mathbf{i}}+\frac{(2-3 \mathbf{i}) \mathbf{y}+\mathbf{i}}{3-\mathbf{i}}=\mathbf{i} \text { are : }\)

1 \(x=-1, x=3\)
2 \(x=3, y=-1\)
3 \(x=0, y=1\)
4 \(\mathrm{x}=1, \mathrm{y}=0\)
BCECE-2003
Complex Numbers and Quadratic Equation

117486 The number of solutions of equation \(\mathrm{z}^2+\overline{\mathrm{z}}=0\), where \(\mathrm{z} \in \mathrm{C}\) are

1 6
2 1
3 4
4 5
Karnataka CET-2012