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Question Number 127261 by mohammad17 last updated on 28/Dec/20

f o r a n y c o m p l e x n u m b e r i f i m (z) > 0

t h e n i m (\frac{1}{z}) > 0 p r o v e t h i s ?

Commented by mr W last updated on 28/Dec/20

w r o n g!

i f i m (z) > 0 t h e n i m (\frac{1}{z}) < 0 .

Answered by mr W last updated on 28/Dec/20

z = a + b i

i m (z) = b > 0

\frac{1}{z} = \frac{1}{a + b i} = \frac{a - b i}{a^{2} + b^{2}}

i m (\frac{1}{z}) = - \frac{b}{a^{2} + b^{2}} < 0

Commented by mohammad17 last updated on 28/Dec/20

t h a n k y o u s i r