Ask Questions, Get Answers

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

Express the following complex numbers in polar form. $-1 - \mathit{i}$

This the third part of the multi-part Q6.

Can you answer this question?

1 Answer

0 votes
  • If $z=x+iy$ is written in exponential form as $z=r(\cos \theta+i\sin \theta),r=\sqrt{x^2+y^2}$ and the argument $\theta$ is given by the following rule
  • $\theta=\pi-\alpha\Rightarrow \theta=\alpha$
  • $\theta=-\pi+\alpha\Rightarrow \theta=-\alpha$
  • Where $\alpha=\tan^{-1}\mid\large\frac{y}{x}\mid$ and $(x,y)$ lies in one of the four quadrants (or the axes).
Step 1:
Let $-1-i=r(\cos \theta+i\sin \theta)$
Therefore $r\cos\theta=-1$ and $r\sin \theta=-1$
Squaring and adding we get
$r=\sqrt{1+1}=\sqrt 2$
Step 2:
The point representing $-1-i$ lies in the quadrant 3
Therefore $\theta=\pi+\alpha=\pi+\large\frac{\pi}{4}=\frac{5\pi}{4}$
answered Jun 10, 2013 by sreemathi.v
edited Jul 19, 2013 by sreemathi.v

Related questions

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