KTU Model Question Paper for MA201 Linear Algebra and Complex Analysis

Linear Algebra and Complex Analysis MA201 Model Question Paper

PART A

1. Find the bilinear transformation which maps points z=1,i,-1 into the path w = i,0,-i. Hence find the image of(z) < 1. 2. Show that the mapping w = 1/z maps every circle onto a circle or a straight line.

3. Evaluate Integral over 'C' 2Z^2+1/(z+1)^2 * (z-2) dz, where C is the circle [z] = 3 integration being taken in anticlockwise direction. 4. Find the taylor series expansion of f[z] = 2z^2+9z+5/z^3+z^2-8z-12 about Zo =1.

PART B

5. Find the image of circle [z] = C not equal 1 under the map w = z+1/z.

6. Determine the linear fractional transformation that maps z1 = 0, z2 =1, z3 = infinite - onto w1 = -1, = -i =w3 = 1 respectively.

7. Evaluate Integral over 'C' z+1/z dz ,C is the unit circle intengration being taken in counterclockwise direction.

8. Find all maclarin's series expansion of f(z)= z^8 /1-z^4.

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