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Complex Number
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Complex Number
All Questions (Page: 7)
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All Questions (PDF)
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Study Material (PDF)
All Questions (PDF)
English Version
Self Assesment
Sort As
Serial Number
Newly Added
Language
English
Click on each question to see answer & solution.
Question No: #61
In complex plane, three points are represented by three complex numbers `z_1, z_2, z_3` and `|z_1| = |z_2| = |z_3| = 1` and `z_1 + z_2 + z_3 = 0`. Then find the area of triangle formed by these three points.
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Question No: #62
In a complex plane three points, represented by three complex numbers `z_1, z_2, z_3` and `\frac{1}{z_1-z_2} + \frac{1}{z_2-z_3} + \frac{1}{z_3-z_1} = 0`. Show that the triangle formed by these three points are equilateral triangle.
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Question No: #63
In a complex plane, the three points `z_1, z_2, z_3` are three vertices of an isosceles right angle triangle with right angle at `z_3`. Then show that `z_1^2 + 2z_2^2 + z_3^2 = 2z_2(z_1 + z_3)`
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Question No: #64
`z_1, z_2` are two complex numbers and `z_1^2 + z_2^2 + 2z_1z_2cos\theta=0`. Then show that the triangle formed by origin, `z_1` and `z_2` is an isosceles triangle. (where `\theta \in \mathbb{R}`)
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Question No: #65
If `z = x+iy`, `w = \frac{1-iz}{z-i}` and `|w|=1`, then show that `z` lies on real axis on the complex plane.
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Question No: #66
Show that the three points `1+4i, 2+7i` and `3+10i` are collinear.
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Question No: #67
If three points `z, -iz` and 1 are collinear, then show that `z` always lies on a circle.
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Question No: #68
If `z = x+iy` and `\text{arg}(\frac{z-1}{z+1})=\pi/2`, then show that locus of `z` in complex plane is a circle.
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Question No: #69
If `z = x+iy` and `\text{arg}(\frac{z-1}{z+1})=\pi/4`, then show that locus of `z` in a complex plane is a circle.
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Question No: #70
If `z_1 = 4+3i`, `z_2 = 7+4i` and `z` is another complex number such that `\text{arg}(\frac{z_1-z}{z-z_2}) = \pi/4`; then show that `|z-6-2i| = \sqrt{5}`
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