if-Z-1-1-i-and-Z-2-i-4-by-using-demover-find-Z-1-Z-2-

Question Number 113983 by mohammad17 last updated on 16/Sep/20

i f Z_{1} = 1 - i a n d Z_{2} = i^{4} b y u s i n g d e m o v e r f i n d \frac{Z_{1}}{Z_{2}} ?

Answered by Dwaipayan Shikari last updated on 16/Sep/20

\frac{Z_{1}}{Z_{2}} = \frac{1 - i}{i^{4}} = 1 - i

Commented by mohammad17 last updated on 16/Sep/20

s i r i w a n t t h i s b y d e m o v e r t h e o r e m

Answered by Dwaipayan Shikari last updated on 16/Sep/20

Z_{1} = \sqrt{2} (\frac{1}{\sqrt{2}} - \frac{1}{\sqrt{2}} i) = \sqrt{2} (c o s \frac{π}{4} - i s i n \frac{π}{4})

Z_{1} = i^{4} = {(c o s \frac{π}{2} + i s i n \frac{π}{2})}^{4} = c o s (4 . \frac{π}{2}) + i s i n (4 . \frac{π}{2}) = 1

\frac{Z_{1}}{Z_{2}} = \frac{\sqrt{2} (c o s \frac{π}{4} - i s i n \frac{π}{4})}{1} = \sqrt{2} (c o s \frac{π}{4} - i s i n \frac{π}{4}) = 1 - i

Commented by mohammad17 last updated on 16/Sep/20

t h a n k y o u s i r