Find the Modulus and Argument of the following Complex numbers.
1). \(3+4i\)
2). \(1+1i\)
3). \(\sqrt{3}+i\)
4). \(-i\)
5). \(4\)
6). \(\displaystyle \frac{1+i}{1-i}\)
7). \(\displaystyle \frac{1}{1-i}\)
8). \(\displaystyle \frac{1+2i}{1-3i}\)
Answers :
1). \(\displaystyle 5,\tan ^{-1}\left(\frac{4}{3}\right)\) 2). \(\displaystyle\sqrt{2},\frac{\pi }{4}\)
3). \(2,\displaystyle \frac{\pi }{6}\) 4). \(1,\displaystyle -\frac{\pi }{2}\)
5). \(4,0\) 6). \(1,\displaystyle\frac{\pi }{2}\) 7). \(\displaystyle\frac{1}{\sqrt{2}},\frac{\pi }{4}\)
8). \(\displaystyle \frac{1}{\sqrt{2}},\frac{3 \pi }{4}\)
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