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Complex Number
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Complex Number
All Questions (Page: 1)
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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: #1
Find the fourth root of `7-24i`
Ans: `\pm 1/sqrt{2}(3-i)`, `\pm 1/sqrt{2}(1+3i)`
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Question No: #2
Show that the three points `1+4i, 2+7i` and `3+10i` are collinear.
Ans:
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Question No: #3
`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}`)
Ans:
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Question No: #4
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)`
Ans:
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Question No: #5
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.
Ans:
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Question No: #6
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.
Ans:
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Question No: #7
The three points in a complex plane are represented by `z_1, z_2, z_3` such that `|z_1| = |z_2| = |z_3|` and they form an equilateral triangle in complex plane. Prove that `z_1 + z_2 + z_3 = 0`
Ans:
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Question No: #8
The three vertices of an equilateral triangle are represented by three complex numbers `z_1, z_2, z_3`. Then show that --
i) `\frac{1}{z_1 - z_2} + \frac{1}{z_2 - z_3} + \frac{1}{z_3 - z_1} = 0`
ii) `z_1^2 + z_2^2 + z_3^2 = z_1z_2 + z_2z_3 + z_3z_1`
Ans:
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Question No: #9
If three points `z, -iz` and 1 are collinear, then show that `z` always lies on a circle.
Ans:
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Question No: #10
Prove that, `\text{amp}(z) - \text{amp}(-z) = \pm\pi` when `\text{amp}(z)` be positive or negetive.
Ans:
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