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

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

Guest Jun 2, 2015

#1
+85805
+10

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
Sort:

#1
+85805
+10

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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