You need to convert the algebraic form `z = x + i*y` into polar form `z = rho*(cos alpha + i*sin alpha)` , such that:
`rho = sqrt(x^2 + y^2)`
Comparing the given algebraic form to standard algebraic form, you may see the the real part misses, hence `x = 0` .
`rho = sqrt(y^2) => rho = 11`
`alpha = tan^(-1)(y/x) => alpha = tan^(-1)(11/0) => alpha = pi/2`
Replacing `11` for `rho` and `pi/2` for alpha yields:
`z = 11*(cos(pi/2) + i*sin(pi/2))`
Hence, converting the algebraic form to polar form yields `z = 11*(cos(pi/2) + i*sin(pi/2)).`
The original form is called the rectangular form.
The other form is the polar or trigonometric form.
We'll transform it into the trigonometric form.
z = a + bi
z = 11i
Re(z) = 0 and Im(z) = 11
The polar form:
z = |z|(cos t + i sin t)
|z| = sqrt[Re(z)^2 + Im(z)^2]
|z| = sqrt (0 + 121)
|z| = 11
tan t = Im (z)/Re(z)
Tan t = 11/0
t = pi/2
The trigonometric form of the complex number is:
z = 11(cos pi/2 + i*sin pi/2)