In the Protocol ‘modern biotechnology’ is referred to as the application of fusion of cells beyond the taxonomic family (called ‘in vitro nucleic acid’ techniques) that overcome natural physiological reproductive or recombination barriers and are not techniques used in traditional breeding and selection. The term Living modified organism (LMO) is defined as the processing of any material that is of LMO origin, containing detectable novel combinations of replicable genetic material obtained through the use of modern biotechnology (for instance, flour from genetically modified maize). The LMOs intended for direct use as food or feed, or for processing are agricultural commodities from genetically modified crops (http://www.gmofreeregions.org/glossary.html Accessed 26.11.16.). Although the Protocol did not use the term genetically modified organism, the LMO is almost equivalent to the GMO, which is any organism whose genetic material has been altered using genetic engineering techniques (i.e., a genetically engineered organism). A more popular name of the GMO is ‘transgenic organism’
SOLVED MTH632 Assignment 1 Solution and Discussion

Fall 2019
MTH632: Complex Analysis and Differential Geometry
Assignment No. 1 (Lectures # 1 to 12) Total Marks: 10
Due Date: Tuesday, November 26, 2019Please read the following instructions before attempting the solution of this assignment:
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 No Assignment will be accepted once the Assignment solutions are uploaded.Question No. 1: Marks: 10
Suppose that f(z)=x^2y^22y+i(2x2xy), where z=x+iy. Use the expressions
x=(z+z ̅)/2 and y=(zz ̅)/2i
to write f(z) in terms of z, and simplify the result. 
Q. 1 Solution:
f(z)=x^2y^22y+i(2x2xy) f(z)=(z+z ̅ )^2/4+(zz ̅ )^2/4+i(zz ̅ )+i(z+z ̅ )(z+z ̅ )(zz ̅ )/2 f(z)=z^2/2+z ̅^2/2+2izz^2/2+z ̅^2/2 f(z)=z ̅^2+2iz  ANSWER

Q. 1 Solution:
f(z)=x^2y^22y+i(2x2xy) f(z)=(z+z ̅ )^2/4+(zz ̅ )^2/4+i(zz ̅ )+i(z+z ̅ )(z+z ̅ )(zz ̅ )/2 f(z)=z^2/2+z ̅^2/2+2izz^2/2+z ̅^2/2 f(z)=z ̅^2+2iz  ANSWER