How to convert a complex number to polar form? Can you explain with an example.

Asked by pksunilnair | 14th Aug, 2016, 11:54: AM

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 | 16th Aug, 2016, 11:07: AM