logo

Ask Questions, Get Answers

 
X
 Search
Want to ask us a question? Click here
Browse Questions
Ad
Home  >>  TN XII Math  >>  Complex Numbers
0 votes

Express the following in the standard form $a + ib$: $\large\frac{2\left ( i-3 \right )}{\left ( 1+i \right )^{2}}$

This is the first part of the Q1 multipart question.

Can you answer this question?
 
 

1 Answer

0 votes
Toolbox:
  • $i^2=-1,i^3=-i,i^4=1$.
  • In general,$i^{4n-3}=i$,$i^{4n-2}=-1$,$i^{4n}=1$
  • If $z=a+ib$ then ,
  • $\bar{z}=a-ib$
  • $\mid z\mid=\sqrt{a^2+b^2}$
  • $z^{-1}=\large\frac{a-ib}{a^2+b^2}$
  • $zz^{-1}=a^2+b^2$
  • Also $Re(z)=a,Im(z)=b$
$\large\frac{2(i-3)}{(1+i)^2}=\large\frac{2(i-3)}{1+2i+i^2}$
$\qquad\quad=\large\frac{2(i-3)}{1+2i-1}$
$\qquad\quad=\large\frac{i-3}{1}$
$\qquad\quad=\large\frac{(i-3)i}{i^2}$
$\qquad\quad=\large\frac{i^2-3i}{-1}$
$\qquad\quad=\large\frac{-1-3i}{-1}$
$\qquad\quad=1+3i$
answered Jun 7, 2013 by sreemathi.v
 

Related questions

Ask Question
student study plans
x
JEE MAIN, CBSE, NEET Mobile and Tablet App
The ultimate mobile app to help you crack your examinations
Get the Android App
...