117832
If \(\left|\mathbf{z}_1\right|=2,\left|\mathbf{z}_2\right|=3,\left|\mathbf{z}_3\right|=4\) and \(\left|2 z_1+3 z_2+4 z_3\right|=4\), then \(\left|8 z_2 z_3+27 z_3 z_1+64 z_1 z_2\right|\) is equal to
117834
The equation \(z \bar{z}+(2-3 i) z+(2+3 i) \bar{z}+4=0\) represents a circle of radius
1 2
2 3
3 4
4 6
Explanation:
B Consider the equation \(z \bar{z}+(2-3 i) z+(2+3 i) \bar{z}+4=0\) Let \(z=x+i y\) and \(\bar{z}=x-i y, \quad z \bar{z}=x^2+y^2\) Put value of \(z, \bar{z}\) and \(z \bar{z}\) in equation (1), we get \(\left(x^2+y^2\right)+(2-3 i)(x+i y)+(2+3 i)(x-i y)+4=0\) \(4 \mathrm{x}+6 \mathrm{y}+4+\mathrm{x}^2+\mathrm{y}^2=0\) \(\mathrm{x}^2+\mathrm{y}^2+4 \mathrm{x}+6 \mathrm{y}+4+9=9\) \((x+2)^2+(y+3)^2=9\) Now, we make it perfect square add both side 9 \(x^2+y^2+4 x+6 y+4+9=9\) \((x+2)^2+(y+3)^2=9\)This represents a circle of radius 3 .
117832
If \(\left|\mathbf{z}_1\right|=2,\left|\mathbf{z}_2\right|=3,\left|\mathbf{z}_3\right|=4\) and \(\left|2 z_1+3 z_2+4 z_3\right|=4\), then \(\left|8 z_2 z_3+27 z_3 z_1+64 z_1 z_2\right|\) is equal to
117834
The equation \(z \bar{z}+(2-3 i) z+(2+3 i) \bar{z}+4=0\) represents a circle of radius
1 2
2 3
3 4
4 6
Explanation:
B Consider the equation \(z \bar{z}+(2-3 i) z+(2+3 i) \bar{z}+4=0\) Let \(z=x+i y\) and \(\bar{z}=x-i y, \quad z \bar{z}=x^2+y^2\) Put value of \(z, \bar{z}\) and \(z \bar{z}\) in equation (1), we get \(\left(x^2+y^2\right)+(2-3 i)(x+i y)+(2+3 i)(x-i y)+4=0\) \(4 \mathrm{x}+6 \mathrm{y}+4+\mathrm{x}^2+\mathrm{y}^2=0\) \(\mathrm{x}^2+\mathrm{y}^2+4 \mathrm{x}+6 \mathrm{y}+4+9=9\) \((x+2)^2+(y+3)^2=9\) Now, we make it perfect square add both side 9 \(x^2+y^2+4 x+6 y+4+9=9\) \((x+2)^2+(y+3)^2=9\)This represents a circle of radius 3 .
117832
If \(\left|\mathbf{z}_1\right|=2,\left|\mathbf{z}_2\right|=3,\left|\mathbf{z}_3\right|=4\) and \(\left|2 z_1+3 z_2+4 z_3\right|=4\), then \(\left|8 z_2 z_3+27 z_3 z_1+64 z_1 z_2\right|\) is equal to
117834
The equation \(z \bar{z}+(2-3 i) z+(2+3 i) \bar{z}+4=0\) represents a circle of radius
1 2
2 3
3 4
4 6
Explanation:
B Consider the equation \(z \bar{z}+(2-3 i) z+(2+3 i) \bar{z}+4=0\) Let \(z=x+i y\) and \(\bar{z}=x-i y, \quad z \bar{z}=x^2+y^2\) Put value of \(z, \bar{z}\) and \(z \bar{z}\) in equation (1), we get \(\left(x^2+y^2\right)+(2-3 i)(x+i y)+(2+3 i)(x-i y)+4=0\) \(4 \mathrm{x}+6 \mathrm{y}+4+\mathrm{x}^2+\mathrm{y}^2=0\) \(\mathrm{x}^2+\mathrm{y}^2+4 \mathrm{x}+6 \mathrm{y}+4+9=9\) \((x+2)^2+(y+3)^2=9\) Now, we make it perfect square add both side 9 \(x^2+y^2+4 x+6 y+4+9=9\) \((x+2)^2+(y+3)^2=9\)This represents a circle of radius 3 .
117832
If \(\left|\mathbf{z}_1\right|=2,\left|\mathbf{z}_2\right|=3,\left|\mathbf{z}_3\right|=4\) and \(\left|2 z_1+3 z_2+4 z_3\right|=4\), then \(\left|8 z_2 z_3+27 z_3 z_1+64 z_1 z_2\right|\) is equal to
117834
The equation \(z \bar{z}+(2-3 i) z+(2+3 i) \bar{z}+4=0\) represents a circle of radius
1 2
2 3
3 4
4 6
Explanation:
B Consider the equation \(z \bar{z}+(2-3 i) z+(2+3 i) \bar{z}+4=0\) Let \(z=x+i y\) and \(\bar{z}=x-i y, \quad z \bar{z}=x^2+y^2\) Put value of \(z, \bar{z}\) and \(z \bar{z}\) in equation (1), we get \(\left(x^2+y^2\right)+(2-3 i)(x+i y)+(2+3 i)(x-i y)+4=0\) \(4 \mathrm{x}+6 \mathrm{y}+4+\mathrm{x}^2+\mathrm{y}^2=0\) \(\mathrm{x}^2+\mathrm{y}^2+4 \mathrm{x}+6 \mathrm{y}+4+9=9\) \((x+2)^2+(y+3)^2=9\) Now, we make it perfect square add both side 9 \(x^2+y^2+4 x+6 y+4+9=9\) \((x+2)^2+(y+3)^2=9\)This represents a circle of radius 3 .
