Answers

2016-03-17T19:44:18+05:30
Let  a complex number (z) = 1/1+i
z= \frac{1(1-i)}{(1+i)(1-i)}  \\ z= \frac{1-i}{ 1^{2} - i^{2} }  \\ z= \frac{1-i}{1-(-1)} = \frac{1-i}{1+1 }  \\ z= \frac{1-i}{2}
now,
z = 1/2 -i/2
 so real part of z = x = 1/2
Imaginary part of z = y = 1/2
|z|= \sqrt{ x^{2} + y^{2} }  \\ |z|= \sqrt{ (1/2)^{2} + (1/2)^{2} }  \\ |z|= \sqrt{ \frac{2}{ 2^{2} } } =  \frac{1}{ \sqrt{2} }

Argument = tan⁻¹(y/x)
Argument = tan^{-1}  \frac{1/2}{1/2}  = tan^{-1}  \frac{1}{1} =   \frac{ \pi }{4}
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