Page 15 - DMTH402_COMPLEX_ANALYSIS_AND_DIFFERENTIAL_GEOMETRY

Complex Analysis and Differential Geometry

Notes 6. Sketch the set of points satisfying
(a) |z – 2 + 3i| = 2 (b) |z + 2i|  1

(c) Re(z i)  4 (d) |z – 1 + 2i| = |z + 3 + i|

(e) |z + 1| + |z – 1| = 4 (f) |z + 1| – |z – 1| = 4
7. Write in polar form re :
i
(a) i (b) 1 + i

(c) –2 (d) –3i
(e) 3  3i

8. Write in rectangular form—no decimal approximations, no trig functions:
(a) 2e i3 (b) e i100
(c) 10e i/6 (d) 2 e i5/4

9. (a) Find a polar form of (1 + i) (1 i 3).

(b) Use the result of a) to find cos   7   and sin   7   .
 12   12 
10. Find the rectangular form of (1 + i) .
100
11. Find all z such that z = 1. (Again, rectangular form, no trig functions.)
3
12. Find all z such that z = 16i. (Rectangular form, etc.)
4
Answers: Self Assessment

1. modulus 2. z = x – iy
3. imaginary part 4. complex numbers

1.7 Further Readings

Books Ahelfors, D.V. : Complex Analysis
Conway, J.B. : Function of one complex variable
Pati, T. : Functions of complex variable
Shanti Narain : Theory of function of a complex Variable
Tichmarsh, E.C. : The theory of functions
H.S. Kasana : Complex Variables theory and applications
P.K. Banerji : Complex Analysis
Serge Lang : Complex Analysis
H.Lass : Vector & Tensor Analysis
Shanti Narayan : Tensor Analysis
C.E. Weatherburn : Differential Geometry
T.J. Wilemore : Introduction to Differential Geometry
Bansi Lal : Differential Geometry.

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