Question

What are the square roots of unity in rectangular and polar form?

Answer 1

Answer:z=1+0i (rectangular coordinate)

z=cos0+sin0 or exp^i0 (polar coordinate)

Explanation:

Unity is 1

Let z be a complex number

z =√1

z=1

z = x + iy(rectangular coordinate)

z=rcos(theta)+isin(theta) (polar coordinate)

For rectangular form, since unity is a real value, x=1 and y=0(no complex value)

z=1+0i (rectangular)

For polar, we need to calculate 'r' and theta.

r=√x^2+y^2

r=√1+0

r=1

theta= arctan(y/x) = arctan(0/1) = 0degree.

z=cos0+sin0 or exp^i0