# changing the formhow to change the original form of z=11i into another form and what is that form?

sciencesolve | Certified Educator

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)).`

giorgiana1976 | Student

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)