Question

Find the reciprocal of the equation in standard form. The selected answer is incorrect.

Answer 1

C

Explanation:

reciprocal of z=1/z

`z=2(cos (\pi )/(4) +i sin(\pi )/(4) )=2e ^{i \frac{\pi } {4}\\(1)/(z)=\frac{1}{2e^{i (\pi)/(4) } }\\(1)/(z) =(1)/(2) e^{-i(\pi)/(4) } \\(1)/(z) (cos(\pi)/(4) -isin(\pi)/(4) ) \\(1)/(z)=(1)/(2) ((√(2) )/(2) -(√(2) )/(2) )\\(1)/(z) =(√(2) )/(4) -i (√(2 ) )/(4)`