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5-Complex Numbers

Complex Numbers

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How to prepare for Complex Numbers for JEE
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2
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20
patelrahul
patelrahul
deveshgarg2008
Geometry and nth Roots of Unity
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4
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21
deveshgarg2008
deveshgarg2008
R
Can you please tell me different approaches for this question? Thanks in advance
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1
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48
solution.livedoubt
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M
If \( (z+1)^{2 n}+(z-1)^{2 n}=0 \), where \( z \) is a complex number and \( n \in N \), then which of the following is always true?
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2
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83
patelrahul
patelrahul
D
Finding the Ratio: Diagonals Intersection in a Pentagon with Parallel Sides
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1
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60
solution.livedoubt
S
Anish
What should be the approach?
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1
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32
solution.livedoubt
S
D
The product of any two of the tenth roots of unity is...?
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1
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39
solution.livedoubt
S
deveshgarg2008
Let $z_1$ and $z_2$ be roots of the equation $z^2+p z+q=0$, where the coefficients p and q may be complex numbers. Let A and B represent $z_1$ and ...
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3
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81
deveshgarg2008
deveshgarg2008
A
Let \( z \) be a complex number satisfying \( \left|z^{2}+2 z \cos \alpha\right| \leq 1 .(\alpha \in R) \) Find maximum value of \(|z+\cos(\alpha)|\).
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1
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49
Math.LiveDoubtClearing
M
deveshgarg2008
  • Solved
If $\omega$ is the imaginary cube root of unity such that
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3
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105
deveshgarg2008
deveshgarg2008
M
If $z=3-4 i$ then $|z|$ is equal to
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1
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57
Math.LiveDoubtClearing
M
L
Among the complex numbers z satisfying the condition $|z+3-\sqrt{3} i|=\sqrt{3}$, find the number having the least positive argument.
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1
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128
Math.LiveDoubtClearing
M
L
Real and imaginary number
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69
Math.LiveDoubtClearing
M
P
If \( 1, \omega, \omega^{2}, \omega^{3} \ldots \ldots, \omega^{n-1} \) are the, \( n^{\text {th }} \) roots of unity, then
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1
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40
Math.LiveDoubtClearing
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SUNIT DAS
Consider an equation \( \left(\frac{z-1}{z}\right)^{2 n}+\left(\frac{z-1}{z}\right)^{n}+1=0 \) (where \( n \in N \) ), then -
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1
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100
Math.LiveDoubtClearing
M
SUNIT DAS
If $w=\frac{z-1}{z-2},|z|=1, z, w \in C$, then -
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1
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68
Math.LiveDoubtClearing
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Ashutosh
For \( a \in \mathbb{C} \), let \( A=\{z \in \mathbb{C}: \operatorname{Re}(a+\bar{z})>\operatorname{Im}(\bar{a}+z)\} \)
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2
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79
Math.LiveDoubtClearing
M
SUNIT DAS
Let \( z \) be a complex number satisfying \( |z|=1 \) and \( |\arg (z)|<\frac{\pi}{3} \) then \( \arg \left(z^{2}+\bar{z}\right)= \)
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3
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96
SUNIT DAS
SUNIT DAS
SUNIT DAS
If \( z_{1}^{2}+\left|z_{1}\right|=z_{2}^{2}+\left|z_{2}\right|=z_{3}^{2}+\left|z_{3}\right|=0\left(z_{1} \neq z_{2} \neq z_{3}\right) \) and ...
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2
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57
SUNIT DAS
SUNIT DAS
Akila
If $\dfrac{a}{\left|z_1-z_2\right|}=\dfrac{b}{\left|z_2-z_1\right|}=\dfrac{c}{\left|z_3-z_1\right|} (a, b, c\in R)$, then ...
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2
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68
LiveDoubtClearing
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Akila
If $z(1+a)=b+i c, a^2+b^2+c^2=1$, then $\frac{1+i z}{1-i z}=$
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1
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68
Math.LiveDoubtClearing
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