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

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

\[4-i\]

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

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