NOUN TMA Questions and Answers: MTH210- Introduction to Complex Analysis

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Richtubor
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NOUN TMA Questions and Answers: MTH210- Introduction to Complex Analysis

Postby Richtubor » Fri Feb 01, 2019 7:45 am

NOUN TMA Questions and Answers: MTH210- Introduction to Complex Analysis


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Q1 Find the quotient \[\frac{(6+i)+(1+3i}{-3+i}\]

\[\frac{-17-19i}{10}\]

Q2 For any complex number and any integer k, \[i^{4k+2}=􀳦?􀳦.\]

-1

Q3 Simplify \[(4-5i)(2+3i)\]

\[23+2i\]

Q4 \[(a+bi)(c+di)=􀳦?􀳦.\]

\[(ac-bd)+(ad+bc)i\]

Q5 \[\frac{z^4-1}{z-i}=􀳦?􀳦􀳦?􀳦.\]

\[z^3+iz^2-z+i\]

Q6 The square of the imaginary number of a complex number has the value

-1

Q7 The Fundamental Theorem of Algebra states that

Every non-constant polynomial with coefficients in th e set of complex numbers, C (or set of real numbers,R) has a root in C

Q8 If in a complex number, \[z=x=iy, x=0\]then z is said to be 􀳦?􀳦􀳦?􀳦􀳦?􀳦.

purely ima ginary

Q9 One of the following is not true about a complex number

The imaginary part of \[3+5i\;is\; 5i\]

Q10 The equation \[x^2+1=0\] has 􀳦?􀳦􀳦?􀳦.. real solutions

no


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Richtubor
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Re: NOUN TMA Questions and Answers: MTH210- Introduction to Complex Analysis

Postby Richtubor » Fri Feb 01, 2019 7:47 am

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Q11 \[If \;z_1 = 2(cos 15 + i sin 15)\; and \;\;z_2 = \frac{1}{2}(cos 30 + i sin 30)\] are complex numbers, then\[ z_1z_2\;= \]

\[cos 45 + i sin 45\]

Q12 Let f(z) =u + v be an analytic function, one of the following statements in not correct

a non constant analytic function can take only real or only p ure imaginary values

Q13 In a complex function \[f(z) =u(x,y) + iv(x,y),\; z + iy\] is analytic in a domain D iff

v is a harmonic conjugate to u in D

Q14 The argument of the cube of a complex number is same as

\[arg z + arg z^2\]
\[arg z + 2 arg z\]
\[3 arg z\]
---All of the options

Q15 One of the following is true about a continuous function

A function f(z) is continuous if it is continuous at all points w here it is defined.
A funcion is continuous if and only if its real and imaginary parts are continuou s
All polynomials P(z) are continuous
---all the options

Q16 All the following are true except

The differences of analytic functions are analytic

Q17 For any complex number z, the argument of its square is given by

\[arg z^2 = 2 arg z\]

Q18 Simplify using Euler's equation: \[(1+i)^24\]

\[2^{12}\]

Q19 Evaluate \[e^{-1}e^\frac{i\pi}{2}\] using Euler􀳦??s equation

\[\frac{i}{e}\]

Q20 Evaluate \[e^{i\pi}\] using Euler􀳦??s equation

-1



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Re: NOUN TMA Questions and Answers: MTH210- Introduction to Complex Analysis

Postby Richtubor » Fri Feb 01, 2019 7:50 am

Q21 Two complex numbers $$(x_1,y_1)$$ and$$(y_2,y_2)$$ are

\[x_{1} = x_{2}\; and\;y_{1} = y_{2}\]

Q22 Suppose\[z = -1-i\sqrt{ 3}\]evaluate \[tan\theta\]

\[\sqt 3\

Q23 Suppose\[z = -1-i\sqrt {3}\]evaluate |z|

2

Q24 \[If \;|z|=2 \]and\[arg(z)=\frac{\pi}{6},\] then z in polar form is given by

\[2 cos\frac{\pi}{6}+ 2 sin\frac{\pi}{6}\ ]

Q25 The imaginary part of \[(1+i)^3\] is􀳦?􀳦􀳦?􀳦.

2

Q26 The real part of \[(1+i)^3\] is􀳦?􀳦􀳦?􀳦.

-2

Q27 If\[w=2-3i\], \[ z=-3-7i ,\]evaluate \[\frac{w}{z}\]

\[\frac{15+23i}{ 58}\]

Q28 Evaluate the modulus of \[ -3-7i \]

\[\sq rt{58}\]

Q29 If\[w=2-3i\], z=-3-7i \]evaluate 3w -2z

\[12+5i\]

Q30 If\[w=3-4i\], z=-2+7i \]evaluate 2w + z

\[4-i\]



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Richtubor
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Re: NOUN TMA Questions and Answers: MTH210- Introduction to Complex Analysis

Postby Richtubor » Fri Feb 01, 2019 7:52 am

Q21 Two complex numbers $$(x_1,y_1)$$ and$$(y_2,y_2)$$ are

\[x_{1} = x_{2}\; and\;y_{1} = y_{2}\]

Q22 Suppose\[z = -1-i\sqrt{ 3}\]evaluate \[tan\theta\]

\[\sqt 3\

Q23 Suppose\[z = -1-i\sqrt {3}\]evaluate |z|

2

Q24 \[If \;|z|=2 \]and\[arg(z)=\frac{\pi}{6},\] then z in polar form is given by

\[2 cos\frac{\pi}{6}+ 2 sin\frac{\pi}{6}\ ]

Q25 The imaginary part of \[(1+i)^3\] is􀳦?􀳦􀳦?􀳦.

2

Q26 The real part of \[(1+i)^3\] is􀳦?􀳦􀳦?􀳦.

-2

Q27 If\[w=2-3i\], \[ z=-3-7i ,\]evaluate \[\frac{w}{z}\]

\[\frac{15+23i}{ 58}\]

Q28 Evaluate the modulus of \[ -3-7i \]

\[\sq rt{58}\]

Q29 If\[w=2-3i\], z=-3-7i \]evaluate 3w -2z

\[12+5i\]

Q30 If\[w=3-4i\], z=-2+7i \]evaluate 2w + z

\[4-i\]



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Richtubor
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Re: NOUN TMA Questions and Answers: MTH210- Introduction to Complex Analysis

Postby Richtubor » Fri Feb 01, 2019 7:55 am

Email: Solutions2tma@gmail.com
Whatsapp: 08155572788


Q31 Let \[z_1=a+ib\; and \;z_2=(a+c)+i(b+d), then\;z_2-z_1=\;􀳦?􀳦...\]

\[c+id\]

Q32 The geometric representation of complex number is the

Argand diagram

Q33 One of these expresses distributive law

\[(z_1+ z_2)z_3=z_1z_3+z_2 z_3\]

Q34 The conjugate of \[x+iy\] is

\[x-iy\]

Q35 Find the modulus of \[z=2+i\]

\[\sqr{5}\]

Q36 The conjugate of the quotient of two complex numbers is the same as

quotient of the conjugates of the two complex numbers provided the denominator is not equal to zero

Q37 The absolute value of the conjugate of a complex number is the 􀳦?􀳦􀳦?􀳦.

absolute value of the complex nu mber

Q38 The conjugate of the conjugate of a complex number is the 􀳦?􀳦􀳦?􀳦.

complex number

Q39 The square of the absolute value has the property

\[(x+iy)(x-iy)\]

Q40 One of these describes associativity of multiplication of complex numbers

\[z_1(z_2z_3)=(z_1z_2)z_3\]




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