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CBSE Class 11-science Answered

Which term of AP 7-4i,6-2i,5-0i,4+2i is purely real and purely imaginary 
Asked by SHAMSUDEEN | 13 Feb, 2015, 05:06: PM
answered-by-expert Expert Answer
G i v e n space A P space i s space 7 minus 4 i comma space 6 minus 2 i comma space 5 minus 0 i comma space 4 plus 2 i comma..... a equals 7 minus 4 i space a n d space d equals 6 minus 2 i minus open parentheses 7 minus 4 i close parentheses rightwards double arrow d equals negative 1 plus 2 i A n d space w e space k n o w space t h a t space t equals a plus open parentheses n minus 1 close parentheses d H e r e comma space r e a l space p a r t space o f space a l l space t h e space t e r m s space f o r m space a n space A P space a n d space t h e space i m a g i n a r y space t e r m s space f o r m space a n space A P T h a t space i s comma space 7 comma 6 comma 5 comma 4 comma... f o r m space a n space A P space a n d space minus 4 comma negative 2 comma 0 comma 2 comma... f o r m space a n space A P C o n s i d e r space t h e space r e a l space p a r t space o f space A P a subscript r e a l end subscript equals 7 semicolon d subscript r e a l end subscript equals 6 minus 7 equals negative 1 A n d a subscript i m a g i n a r y end subscript equals negative 4 d subscript i m a g i n a r y end subscript equals negative 2 minus open parentheses negative 4 close parentheses equals 4 minus 2 equals 2 O u r space a i m space i s space t o space f i n d space t h e space t e r m s space o f space A P space w h i c h space i s space p u r e l y space r e a l space a n d space p u r e l y space i m a g i n a r y. W e space n e e d space t o space f i n d space n comma space w h o s e space n t h space t e r m space o f space i m a g i n a r y space p a r t space o f space A P space i s space z e r o. F r o m space t h e space g i v e n space A P space i t space i s space c l e a r space t h a t space 3 r d space t e r m space o f space i m a g i n a r y space p a r t space o f space A P space i s space z e r o. H e n c e space t h e space t e r m space w h i c h space i s space p u r e l y space r e a l comma space i s space 5 minus 0 i W e space n e e d space t o space f i n d space n comma space w h o s e space n t h space t e r m space o f space r e a l space p a r t space o f space A P space i s space z e r o. t subscript n equals a subscript r e a l end subscript plus open parentheses n minus 1 close parentheses d subscript r e a l end subscript rightwards double arrow 0 equals 7 plus open parentheses n minus 1 close parentheses open parentheses negative 1 close parentheses rightwards double arrow 7 minus n plus 1 equals 0 rightwards double arrow 8 minus n equals 0 rightwards double arrow n equals 8 T h u s comma space s u b s t i t u t i n g space n equals 8 comma space space a equals 7 minus 4 i space a n d space d equals negative 1 plus 2 i space i n space t h e space f o l l o w i n g space n t h space t e r m comma space w e space h a v e comma t equals a plus open parentheses n minus 1 close parentheses d rightwards double arrow t equals space 7 minus 4 i space plus open parentheses 8 minus 1 close parentheses open parentheses negative 1 plus 2 i space close parentheses rightwards double arrow t equals space 7 minus 4 i space plus 7 open parentheses negative 1 plus 2 i space close parentheses rightwards double arrow t equals space 7 minus 4 i space minus 7 plus 14 i rightwards double arrow t equals 14 i minus 4 i rightwards double arrow t equals 10 i rightwards double arrow t equals 0 plus 10 i space i s space t e r m space w h i c h space i s space p u r e l y space i m a g i n a r y.
Answered by Vimala Ramamurthy | 14 Feb, 2015, 10:01: AM

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