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CBSE Class 11-science Answered

Express the following in polar form:
 
tan alpha minus i
Asked by manasd | 31 Dec, 2015, 10:10: PM
answered-by-expert Expert Answer
C o n s i d e r space t h e space g i v e n space c o m p l e x space n u m b e r z equals tan alpha minus i H e r e comma space R e open parentheses z close parentheses equals tan alpha space a n d space I m open parentheses z close parentheses equals negative 1 T h u s comma space w e space h a v e comma r equals open vertical bar z close vertical bar space space equals square root of open parentheses R e close parentheses squared plus open parentheses I m close parentheses squared end root space space space equals square root of open parentheses tan alpha close parentheses squared plus open parentheses negative 1 close parentheses squared end root space space space equals square root of t a n squared alpha plus 1 end root space space space equals s e c alpha theta equals a r g open parentheses z close parentheses space space equals tan to the power of negative 1 end exponent open parentheses fraction numerator I m open parentheses z close parentheses over denominator R e open parentheses z close parentheses end fraction close parentheses space space space equals t a n to the power of negative 1 end exponent open parentheses fraction numerator negative 1 over denominator t a n alpha end fraction close parentheses space space space equals t a n to the power of negative 1 end exponent open parentheses negative c o t alpha close parentheses space space space equals t a n to the power of negative 1 end exponent open parentheses tan open parentheses straight pi over 2 plus alpha close parentheses close parentheses space space space space equals straight pi over 2 plus alpha T h u s comma space t h e space p o l a r space f o r m space i s colon z equals r open parentheses cos theta plus i sin theta close parentheses space space equals s e c alpha open square brackets cos open parentheses straight pi over 2 plus alpha close parentheses plus i sin open parentheses straight pi over 2 plus alpha close parentheses close square brackets
Answered by Vimala Ramamurthy | 01 Jan, 2016, 09:46: AM

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