117506
If the complex numbers \(z_1, z_2\) and \(z_3\) are in \(A P\), then they lie on a
1 a circle
2 a parabola
3 line
4 ellipse
Explanation:
C \(\mathrm{z}_1, \mathrm{z}_2, \mathrm{z}_3 \rightarrow \mathrm{AP}\) (mid point) \(\mathrm{z}_2=\frac{\mathrm{z}_1+\mathrm{z}_3}{2}\) and, \(z_1, z_2, z_3\) are collinear \(\Rightarrow \mathrm{z}_1, \mathrm{z}_2\), and \(\mathrm{z}_3\) lies on a line. \(\Rightarrow \mathrm{A}, \mathrm{B}\) and \(\mathrm{C}\) are collinear. \(\therefore \mathrm{z}_1, \mathrm{z}_2\) and \(\mathrm{z}_3\) lie on a line.
VITEEE-2012
Complex Numbers and Quadratic Equation
117507
Amplitude of \(\frac{1+\sqrt{3} i}{\sqrt{3}+1}\) is:
117506
If the complex numbers \(z_1, z_2\) and \(z_3\) are in \(A P\), then they lie on a
1 a circle
2 a parabola
3 line
4 ellipse
Explanation:
C \(\mathrm{z}_1, \mathrm{z}_2, \mathrm{z}_3 \rightarrow \mathrm{AP}\) (mid point) \(\mathrm{z}_2=\frac{\mathrm{z}_1+\mathrm{z}_3}{2}\) and, \(z_1, z_2, z_3\) are collinear \(\Rightarrow \mathrm{z}_1, \mathrm{z}_2\), and \(\mathrm{z}_3\) lies on a line. \(\Rightarrow \mathrm{A}, \mathrm{B}\) and \(\mathrm{C}\) are collinear. \(\therefore \mathrm{z}_1, \mathrm{z}_2\) and \(\mathrm{z}_3\) lie on a line.
VITEEE-2012
Complex Numbers and Quadratic Equation
117507
Amplitude of \(\frac{1+\sqrt{3} i}{\sqrt{3}+1}\) is:
117506
If the complex numbers \(z_1, z_2\) and \(z_3\) are in \(A P\), then they lie on a
1 a circle
2 a parabola
3 line
4 ellipse
Explanation:
C \(\mathrm{z}_1, \mathrm{z}_2, \mathrm{z}_3 \rightarrow \mathrm{AP}\) (mid point) \(\mathrm{z}_2=\frac{\mathrm{z}_1+\mathrm{z}_3}{2}\) and, \(z_1, z_2, z_3\) are collinear \(\Rightarrow \mathrm{z}_1, \mathrm{z}_2\), and \(\mathrm{z}_3\) lies on a line. \(\Rightarrow \mathrm{A}, \mathrm{B}\) and \(\mathrm{C}\) are collinear. \(\therefore \mathrm{z}_1, \mathrm{z}_2\) and \(\mathrm{z}_3\) lie on a line.
VITEEE-2012
Complex Numbers and Quadratic Equation
117507
Amplitude of \(\frac{1+\sqrt{3} i}{\sqrt{3}+1}\) is:
117506
If the complex numbers \(z_1, z_2\) and \(z_3\) are in \(A P\), then they lie on a
1 a circle
2 a parabola
3 line
4 ellipse
Explanation:
C \(\mathrm{z}_1, \mathrm{z}_2, \mathrm{z}_3 \rightarrow \mathrm{AP}\) (mid point) \(\mathrm{z}_2=\frac{\mathrm{z}_1+\mathrm{z}_3}{2}\) and, \(z_1, z_2, z_3\) are collinear \(\Rightarrow \mathrm{z}_1, \mathrm{z}_2\), and \(\mathrm{z}_3\) lies on a line. \(\Rightarrow \mathrm{A}, \mathrm{B}\) and \(\mathrm{C}\) are collinear. \(\therefore \mathrm{z}_1, \mathrm{z}_2\) and \(\mathrm{z}_3\) lie on a line.
VITEEE-2012
Complex Numbers and Quadratic Equation
117507
Amplitude of \(\frac{1+\sqrt{3} i}{\sqrt{3}+1}\) is: