How do i express -1+(root3)i in polar form?

Question

How do i express -1+(root3)i in polar form?

Answer 1

Let z= -1 + √(3) i

|z|

= √ [ (-1)^2 +√(3)^2]

= 2

Arg (z)

= arctan [√(3) / (-1)]

= arctan [-√(3)]

= -п / 3    OR     2п /3, as  -п < Arg (z) ≤ п

In case you are not familiar with arctan, it simply means inverse tan (i.e. tan^ -1)

We can clearly see on the Argand diagram that...

z = -1 + √(3) i

...lies in the second quandrant, suggesting that;

0  Ã¢Â‰Â¤ Arg (z) ≤ п

Therefore, Arg (z) = 2п /3

The polar form of...  

-1 + √(3) i  

...is...

2cis( 2п /3 )

Answer 2

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