Find the polar form of complex number tan alpha minus i

 

Asked by Topperlearning User | 12th Sep, 2016, 03:27: AM

Expert Answer:

 tan alpha minus i equals r open parentheses cos theta plus i sin theta close parentheses
r cos theta equals tan alpha space a n d space r sin theta equals negative 1 space space space space.... left parenthesis 1 right parenthesis
rightwards double arrow r squared cos squared theta plus r squared sin squared theta equals tan squared alpha plus 1
rightwards double arrow r squared equals s e c squared alpha
rightwards double arrow r equals s e c alpha
P u t t i n g space t h e space v a l u e space o f space r space i n space t h e space e q u a t i o n space left parenthesis 1 right parenthesis comma space w e space g e t comma
cos theta equals sin alpha space a n d space sin theta equals negative cos alpha
N o w space t h e space v a l u e space o f space theta space w h i c h space s a t i s f i e s space t h e space a b o v e space e q u a t i o n space i s space g i v e n space b y
theta equals alpha minus straight pi over 2
H e n c e comma space
tan alpha minus i equals s e c alpha open parentheses cos open parentheses alpha minus straight pi over 2 close parentheses plus i sin open parentheses alpha minus straight pi over 2 close parentheses close parentheses
w h i c h space i s space t h e space r e q u i r e d space p o l a r space f o r m.

Answered by  | 12th Sep, 2016, 05:27: AM