Complex Numbers And Quadratic Equations question 409
Question: $ ( \frac{1}{1-2i}+\frac{3}{1+i} )( \frac{3+4i}{2-4i} )= $ [Roorkee 1979; RPET 1999; Pb. CET 2003]
Options:
A) $ \frac{1}{2}+\frac{9}{2}i $
B) $ \frac{1}{2}-\frac{9}{2}i $
C) $ \frac{1}{4}-\frac{9}{4}i $
D) $ \frac{1}{4}+\frac{9}{4}i $
Show Answer
Answer:
Correct Answer: D
Solution:
$ ( \frac{1}{1-2i}+\frac{3}{1+i} )( \frac{3+4i}{2-4i} ) $ $ =[ \frac{1+2i}{1^{2}+2^{2}}+\frac{3-3i}{1^{2}+1^{2}} ][ \frac{6-16+12i+8i}{2^{2}+4^{2}} ] $ $ =( \frac{2+4i+15-15i}{10} )( \frac{-1+2i}{2} ) $ $ =\frac{(17-11i)(-1+2i)}{20}=\frac{5+45i}{20}=\frac{1}{4}+\frac{9}{4}i $ .
BETA
