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Question Number 201629 by ali009 last updated on 09/Dec/23

Commented by ali009 last updated on 09/Dec/23

$h o w i s t h a t c s l c u l a t e d ?$
Commented by aleks041103 last updated on 09/Dec/23

$A s f a r a s I c a n t e l l t h i s i s a n e l e c t r i c a l$ $e n g e n e e r i n g p r o b l e m .$ $I n E E t h e y u s e j i n s t e a d o f i f o r t h e$ $i m a g i n a r y u n i t \sqrt{- 1} .$ $O t h e r w i s e i t i s s i m p l e d i v i s i o n o f c o m p l e x$ $n u m b e r s .$ $T h e m o s t^{'} {d i f f i c u l t}^{'} p a r t h e r e i s t a k i n g$ $t h e s q u a r e r o o t o f a c o m p l e x n u m b e r .$ $G e n e r a l l y w e u s e t h e p o l a r f o r m i n s u c h$ $c a s e s .$ $z = a + b j = {r e}^{j θ}$ $w h e r e r = \sqrt{a^{2} + b^{2}} a n d θ = a r c t a n (b / a) .$ $T h e n$ $\sqrt{a + b j} = \sqrt{{r e}^{j θ}} = \sqrt{r} e^{j θ / 2}$ $N o w u s i n g {E u l e r}^{'} s f o r m u l a$ $\sqrt{a + b j} = \sqrt{r} (c o s (θ / 2) + i s i n (θ / 2)) =$ $= \sqrt{r} c o s (θ / 2) + i \sqrt{r} s i n (θ / 2)$ $w h e r e a g a i n r = \sqrt{a^{2} + b^{2}} a n d θ = a r c t a n (b / a) .$ $T h e r e s t i s j u s t c r u n c h i n g t h e n u m b e r s .$
Commented by ali009 last updated on 10/Dec/23

$t h a n k y o u s o m u c h a n d r i g h t t h i s i s$ $c o m m u n i c a t i o n e n g e n n i r i n g p r o b l e m$
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