Argand Plane and Polar Representation
Complex Numbers and Quadratic Equation

117980 Let the point \(P\) represent \(z=x+i y, x, y \in R\) in the argand plane. Let the curves \(C_1\) and \(C_2\) be the loci of \(P\) satisfying the conditions
(i) \(\frac{2 z+i}{z-2}\) is purely imaginary and
(ii) \(\operatorname{Arg}\left(\frac{z+i}{z+1}\right)=\frac{\pi}{2}\) respectively. Then the point of intersection of the curves \(C_1\) and \(\mathrm{C}_2\), other than the origin, is

1 \((1,2)\)
2 \(\left(\frac{2}{7},-\frac{5}{7}\right)\)
3 \((-3,4)\)
4 \(\left(\frac{5}{37},-\frac{30}{37}\right)\)
Complex Numbers and Quadratic Equation

117981 Area of the triangle formed by the complex numbers \(z\), iz and \(z+i z\) in the Argand diagram as vertices is

1 \(\frac{1}{2} \cdot|z|^2\)
2 \(\frac{1}{2} \cdot \mathrm{z}^2\)
3 \(z^2\)
4 \(|z|^2\)
Complex Numbers and Quadratic Equation

117982 The point \(\mathrm{z}\) moves on the Argand diagram such that \(|z-3 i|=2\), then its locus is

1 \(y\)-axis
2 a straight line
3 a circle
4 None of these
Complex Numbers and Quadratic Equation

117983 Let \(A(3-i), B(2+i)\) be two points in the argand plane. If the point \(P\) represents the complex number \(z=x+i y\), which satisfies \(|z-3+i|=\mid z\) -2 - \(\mid\), then the locus of the point \(P\) is

1 The circle with \(\mathrm{AB}\) as diameter
2 The line passing through \(A\) and \(B\)
3 The perpendicular bisector of \(A B\)
4 The ellipse with \(\mathrm{AB}\) as major axis
Complex Numbers and Quadratic Equation

117980 Let the point \(P\) represent \(z=x+i y, x, y \in R\) in the argand plane. Let the curves \(C_1\) and \(C_2\) be the loci of \(P\) satisfying the conditions
(i) \(\frac{2 z+i}{z-2}\) is purely imaginary and
(ii) \(\operatorname{Arg}\left(\frac{z+i}{z+1}\right)=\frac{\pi}{2}\) respectively. Then the point of intersection of the curves \(C_1\) and \(\mathrm{C}_2\), other than the origin, is

1 \((1,2)\)
2 \(\left(\frac{2}{7},-\frac{5}{7}\right)\)
3 \((-3,4)\)
4 \(\left(\frac{5}{37},-\frac{30}{37}\right)\)
Complex Numbers and Quadratic Equation

117981 Area of the triangle formed by the complex numbers \(z\), iz and \(z+i z\) in the Argand diagram as vertices is

1 \(\frac{1}{2} \cdot|z|^2\)
2 \(\frac{1}{2} \cdot \mathrm{z}^2\)
3 \(z^2\)
4 \(|z|^2\)
Complex Numbers and Quadratic Equation

117982 The point \(\mathrm{z}\) moves on the Argand diagram such that \(|z-3 i|=2\), then its locus is

1 \(y\)-axis
2 a straight line
3 a circle
4 None of these
Complex Numbers and Quadratic Equation

117983 Let \(A(3-i), B(2+i)\) be two points in the argand plane. If the point \(P\) represents the complex number \(z=x+i y\), which satisfies \(|z-3+i|=\mid z\) -2 - \(\mid\), then the locus of the point \(P\) is

1 The circle with \(\mathrm{AB}\) as diameter
2 The line passing through \(A\) and \(B\)
3 The perpendicular bisector of \(A B\)
4 The ellipse with \(\mathrm{AB}\) as major axis
NEET Test Series from KOTA - 10 Papers In MS WORD WhatsApp Here
Complex Numbers and Quadratic Equation

117980 Let the point \(P\) represent \(z=x+i y, x, y \in R\) in the argand plane. Let the curves \(C_1\) and \(C_2\) be the loci of \(P\) satisfying the conditions
(i) \(\frac{2 z+i}{z-2}\) is purely imaginary and
(ii) \(\operatorname{Arg}\left(\frac{z+i}{z+1}\right)=\frac{\pi}{2}\) respectively. Then the point of intersection of the curves \(C_1\) and \(\mathrm{C}_2\), other than the origin, is

1 \((1,2)\)
2 \(\left(\frac{2}{7},-\frac{5}{7}\right)\)
3 \((-3,4)\)
4 \(\left(\frac{5}{37},-\frac{30}{37}\right)\)
Complex Numbers and Quadratic Equation

117981 Area of the triangle formed by the complex numbers \(z\), iz and \(z+i z\) in the Argand diagram as vertices is

1 \(\frac{1}{2} \cdot|z|^2\)
2 \(\frac{1}{2} \cdot \mathrm{z}^2\)
3 \(z^2\)
4 \(|z|^2\)
Complex Numbers and Quadratic Equation

117982 The point \(\mathrm{z}\) moves on the Argand diagram such that \(|z-3 i|=2\), then its locus is

1 \(y\)-axis
2 a straight line
3 a circle
4 None of these
Complex Numbers and Quadratic Equation

117983 Let \(A(3-i), B(2+i)\) be two points in the argand plane. If the point \(P\) represents the complex number \(z=x+i y\), which satisfies \(|z-3+i|=\mid z\) -2 - \(\mid\), then the locus of the point \(P\) is

1 The circle with \(\mathrm{AB}\) as diameter
2 The line passing through \(A\) and \(B\)
3 The perpendicular bisector of \(A B\)
4 The ellipse with \(\mathrm{AB}\) as major axis
Complex Numbers and Quadratic Equation

117980 Let the point \(P\) represent \(z=x+i y, x, y \in R\) in the argand plane. Let the curves \(C_1\) and \(C_2\) be the loci of \(P\) satisfying the conditions
(i) \(\frac{2 z+i}{z-2}\) is purely imaginary and
(ii) \(\operatorname{Arg}\left(\frac{z+i}{z+1}\right)=\frac{\pi}{2}\) respectively. Then the point of intersection of the curves \(C_1\) and \(\mathrm{C}_2\), other than the origin, is

1 \((1,2)\)
2 \(\left(\frac{2}{7},-\frac{5}{7}\right)\)
3 \((-3,4)\)
4 \(\left(\frac{5}{37},-\frac{30}{37}\right)\)
Complex Numbers and Quadratic Equation

117981 Area of the triangle formed by the complex numbers \(z\), iz and \(z+i z\) in the Argand diagram as vertices is

1 \(\frac{1}{2} \cdot|z|^2\)
2 \(\frac{1}{2} \cdot \mathrm{z}^2\)
3 \(z^2\)
4 \(|z|^2\)
Complex Numbers and Quadratic Equation

117982 The point \(\mathrm{z}\) moves on the Argand diagram such that \(|z-3 i|=2\), then its locus is

1 \(y\)-axis
2 a straight line
3 a circle
4 None of these
Complex Numbers and Quadratic Equation

117983 Let \(A(3-i), B(2+i)\) be two points in the argand plane. If the point \(P\) represents the complex number \(z=x+i y\), which satisfies \(|z-3+i|=\mid z\) -2 - \(\mid\), then the locus of the point \(P\) is

1 The circle with \(\mathrm{AB}\) as diameter
2 The line passing through \(A\) and \(B\)
3 The perpendicular bisector of \(A B\)
4 The ellipse with \(\mathrm{AB}\) as major axis