Test Details

Complex Numbers and Quadratic Equations

Test-02 complex no

Feb 24, 12:00 AM

60 minutes

Feb 24, 1:00 AM

60.0 marks

MCQ

30 questions

J prakash

Diploma in computer science and engineering. B.sc in physics hons. Cisco certified engg.

Class Details

Communication skills

Applied mathematics

Applied Physics

Engineering Graphics

Applied Chemistry

1st Semester Group A

Communication skills

Applied mathematics

Applied Physics

Engineering Graphics

Applied Chemistry

only for gr A student.

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Question Text

Question 1 :
If $n$ is any positive integer, then the value of $\displaystyle \frac{i^{4n+1}-i^{4n-1}}{2}$ equals:

Question 2 :
Express the following complex numbers in the standard from $ a+ib$ : $ \dfrac{5+\sqrt{2}i}{1-\sqrt{2}i}$

Question 4 :
If $z_1, z_2, \varepsilon C$ are such that $|z_1 + z_2|^2 = |z_1|^2 + |z_2|^2$ then $\displaystyle \frac{z_1}{z_2}$ is

Question 5 :
 lf $Z_{1},Z_{2}$ are two unimodular Complex numbers then $ \left |\displaystyle \frac{1}{Z_{1}}+\frac{1}{Z_{2}} \right|=$

Question 8 :
Find the complex numbers z which simultaneously satisfy the equation $\displaystyle \left | \frac{z - 12}{z - 8 i} \right | = \frac{5}{3}$ and $\displaystyle \left | \frac{z - 4}{z - 8} \right | = 1$.

Question 10 :
Modulus of $\dfrac{\cos \theta - i\sin \theta}{\sin \theta - i \cos \theta}$ is

Question 11 :
The simplified form of ${ i }^{ n }+{ i }^{ n+1 }+{ i }^{ n+2 }+{ i }^{ n+3 }$ is

Question 12 :
If $\mid z^2 - 3\mid = 3\mid z\mid$ then the maximum value of $\mid z\mid$ is

Question 13 :
The value of $\displaystyle \sum_{n=1}^{13}{(i^n + i^{n+1})}, i = \sqrt{-1}$, is

Question 14 :
If $|z_1+z_2|=|z_1|+|z_2|$ where $z_1$ and $z_2$ are different non - zero complex number, then ?

Question 15 :
Find the value of $1 + i^2 + i^4 + i^6 + ... + i^{2n}$ 

Question 19 :
The modulus of (1 + i) (1 + 2i) (1 + 3i) is equal to

Question 22 :
The complex number $z$ satisfies $z+|z|=2+8i$. The value of $|z|$ is

Question 23 :
If $a$ and $b$ are integers then $\sqrt a \times \sqrt b=\sqrt {ab}$ is true only when

Question 24 :
Let z be a complex number such that $\left|\dfrac{z-i}{z+2i}\right|=1$ and $|z|=\dfrac{5}{2}$. Then the value of $|z+3i|$ is?

Question 25 :
If z is a complex number such that $\left|\dfrac{z-3i}{z+3i}\right|=1$ then z lies on?

Question 26 :
If $z = \dfrac {(\sqrt {3} + i)^{3} (3i + 4)^{2}}{(8 + 6i)^{2}}$, then $|z|$ is equal to

Question 27 :
If $\begin{vmatrix}6i & -3i & 1\\4 & 3i & -1\\20 & 3 & i\end{vmatrix} = x+ iy$, then 

Question 28 :
if $\displaystyle\ z=1+i\ \tan \alpha $, where $\displaystyle\ \pi < \alpha < \frac{3\pi }{2}$ is $|z|$ is equal to

Question 29 :
The value of the sum $\displaystyle \sum_{n = 1}^{10}(i^n + i^{n + 1})$, where $i = \sqrt{-1}$, equals

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