Write z=-6+6i in polar form

Answer 1

To convert from rectangular form to polar form, we use the following formulas:

magnitude (r) = sqrt(x^2 + y^2)
angle (theta) = tan^-1(y/x)

In this case, we have:

x = -6
y = 6

So:

r = sqrt((-6)^2 + 6^2) = 6*sqrt(2)
theta = tan^-1(6/-6) = -45 degrees or -pi/4 radians (since the point is in the third quadrant)

Therefore, z = 6*sqrt(2) * e^(-i*pi/4) in polar form.

Answer 2

write x=9-3*sqrt3 i in polar form

Answer 3

To convert from rectangular form to polar form, we use the following formulas:

magnitude (r) = sqrt(x^2 + y^2)
angle (theta) = tan^-1(y/x)

In this case, we have:

x = 9
y = -3sqrt(3)

So:

r = sqrt(9^2 + (-3sqrt(3))^2) = sqrt(108) = 6sqrt(3)
theta = tan^-1((-3sqrt(3))/9) = -30 degrees or -pi/6 radians (since the point is in the fourth quadrant)

Therefore, x = 6sqrt(3) * e^(-i*pi/6) in polar form.