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CBSE Class 11-science Answered

How to convert a complex number to polar form? Can you explain with an example.
Asked by pksunilnair | 14 Aug, 2016, 11:54: AM
answered-by-expert Expert Answer
Let space straight x plus iy space be space any space comples space number. Substitute space straight x space equals space rcosθ space space and space straight y equals space rsinθ space then space we space get space the space polar space form space as comma straight x plus iy space equals space straight r open parentheses cosθ plus isinθ close parentheses space Where space straight r squared equals straight x squared plus straight y squared space and space tanθ space equals space straight y over straight x Eaxmple colon Let space us space convert space 1 plus straight i square root of 3 space to space polar space form. Here space straight x space equals space 1 space and space straight y space equals square root of 3 rightwards double arrow 1 space equals space space rcosθ space space and space square root of 3 equals space rsinθ space straight r squared equals straight x squared plus straight y squared equals 1 squared plus open parentheses square root of 3 close parentheses squared equals 1 plus 3 equals 4 therefore straight r equals 2 space tanθ space equals space straight y over straight x equals fraction numerator square root of 3 over denominator 1 end fraction equals square root of 3 rightwards double arrow straight theta equals straight pi over 3 so space the space polar space form space of space 1 plus straight i square root of 3 space is comma 1 plus straight i square root of 3 equals space straight r open parentheses cosθ plus isinθ close parentheses space equals 2 open parentheses cos open parentheses straight pi over 3 close parentheses plus isin open parentheses straight pi over 3 close parentheses close parentheses
Answered by Vijaykumar Wani | 16 Aug, 2016, 11:07: AM

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