Assignment sheet. IV

# Assignment sheet. IV - BIRLA INSTITUTE OF TECHNOLOGY...

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II Semester 2005-2006, Math C 192 Mathematics II Assignment sheet for Quiz IV Q.1 Prove the inequality | z 1 - z 2 | | | z 1 |- |z 2 | | for z 1 & z 2 any complex numbers. . Q.2 Using the fact | z 1 - z 2 | represents distance between complex numbers z 1 & z 2 Prove equation ellispse. an represents , 3 | | | | = + + - i z i z i ii 3 -1 z ) ( i 1 i - 1 z (i) if Argz and z arg Find Q.3 + = + = Q.4 Find all complex numbers for which (1+z)/(1-z) , z 1., is (i) purely imaginary (ii) purely real Q.5 Draw the following sets . Are they open/closed , bounded/ unbounded, which of these Are domain (i) { z: Re(iz)<1} (ii) { z : |z-1|>|z+1| } (iii) { z : |z-i| |z+i| } Q.6 Write the function f(z) = z 3 + 3 1 z , z 0 , in the form f(z) = u(r, θ ) +i v(r, θ ) Q.7 Write the function f(z) = 1 3 - + z i z , z 1/3 , in the form f(z) = u(x,y) +i v(x, y) Q.8 Does | | ) Re( lim 2 2 0 z z z exist ? Justify your answer . (no use y= m x)

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Assignment sheet. IV - BIRLA INSTITUTE OF TECHNOLOGY...

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