Let z =-3+3i

Question

Find r and Q. Drow the angle Q and leave the answer in polar form

Answer 1

To find the polar form of a complex number, we can use the formulas:

r = √(x^2 + y^2)
Q = arctan(y/x)

Given z = -3 + 3i, we can find the values of x and y:

x = -3
y = 3

Using these values, we can calculate r:

r = √((-3)^2 + 3^2)
= √(9 + 9)
= √18

Next, we can calculate Q:

Q = arctan(3/-3)
= arctan(-1)

Note: We are working in the second quadrant, where x is negative and y is positive.

Now, let's find the angle in radians using the arctan function:

Q ≈ -0.7854 radians

Therefore, the polar form of z is:

z = √18 * (cos(-0.7854) + i*sin(-0.7854))

The angle Q can be represented on the complex plane as a line making an angle of -0.7854 radians with the positive x-axis in the second quadrant.