In: Math
Find the 4th roots of i. Sketch them in an Argand diagram.
We need to find solution of the equation
where
is a complex number.
.
Since
is a non negative real number, therefore,
Using Euler's form:
(1) By Euler's formula:
(2)
By equation (1) and (2),
, so,
The values of
give 4 roots of unity.
The 4th roots of unity:
The points (1,0), (-1,0), (0,1), (0,-1) are 4th roots of unity in argand plane.