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how to find a polar form of v in v=4-4i?

 Jun 2, 2015

Best Answer 

 #1
avatar+128085 
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The polar form can be written as....  z = r (cos Θ + i*sinΘ )

 

r = √[(4)^2 + (-4)^2]  = √[16 + 16] = 4√2

 

And  Θ   =  tan-1(-4/4) = tan-1(-1)  = -pi/4    ...so we have

 

z = 4√2 ( cos (-pi/4) +  i*sin (-pi/4) )  

 

..... note that this is the principal value......any angle of the form -pi/4  +  2pi (n)  is also possible, where n is an integer

 

 

 Jun 2, 2015
 #1
avatar+128085 
+10
Best Answer

The polar form can be written as....  z = r (cos Θ + i*sinΘ )

 

r = √[(4)^2 + (-4)^2]  = √[16 + 16] = 4√2

 

And  Θ   =  tan-1(-4/4) = tan-1(-1)  = -pi/4    ...so we have

 

z = 4√2 ( cos (-pi/4) +  i*sin (-pi/4) )  

 

..... note that this is the principal value......any angle of the form -pi/4  +  2pi (n)  is also possible, where n is an integer

 

 

CPhill Jun 2, 2015

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