Which of the following is NOT a root of z^2 = 1-sqrt3i to the nearest hundreth.

a) -0.22+1.24i
b) -0.97-0.81i
c) 1.02-0.65i
d) 1.18-0.43i

Thanks for any help you can give me.

I don't get it. NONE of those numbers, when squared, give you anything close to 1 - i sqrt3. In polar form r(e^i theta), the magnitude r of a valid answer would have to be 2. None of the four choices comes close.

I agree with drwls.

I simply squared some of your answers and should have gotten 1-√3i

none worked, so none are roots.

To find the roots of the equation z^2 = 1 - sqrt(3)i, we can rewrite it as:

z^2 + sqrt(3)i = 1

Let's solve this equation step by step.

Step 1: Move the constant term to the other side

z^2 + sqrt(3)i - 1 = 0

Step 2: Apply the quadratic formula

The quadratic formula is given by:

z = (-b ± sqrt(b^2 - 4ac))/(2a)

In this case, a = 1, b = sqrt(3)i and c = -1.

Substituting these values into the formula, we get:

z = ( - sqrt(3)i ± sqrt( (sqrt(3)i)^2 - 4(1)(-1) ) ) / (2(1))

Simplifying the expression within the square root:

z = ( - sqrt(3)i ± sqrt( -3 + 4 ) ) / 2

z = ( - sqrt(3)i ± sqrt(1) ) / 2

z = ( - sqrt(3)i ± 1 ) / 2

Step 3: Find the roots

Now we have two possible roots:

z_1 = ( - sqrt(3)i + 1 ) / 2
z_2 = ( - sqrt(3)i - 1 ) / 2

To check which option is not a root of the equation, we can substitute each option into our equations and see if they satisfy the original equation.

Let's evaluate each given option:

a) z = -0.22 + 1.24i
Substitute this value into the equation:
LHS = (-0.22 + 1.24i)^2
= -1.4028 - 0.5416i
RHS = 1 - sqrt(3)i
Since LHS ≠ RHS, option a) is not a root of the equation.

b) z = -0.97 - 0.81i
Substitute this value into the equation:
LHS = (-0.97 - 0.81i)^2
= -1.9723 + 1.5747i
RHS = 1 - sqrt(3)i
Since LHS ≠ RHS, option b) is not a root of the equation.

c) z = 1.02 - 0.65i
Substitute this value into the equation:
LHS = (1.02 - 0.65i)^2
= -0.1219 + 2.0393i
RHS = 1 - sqrt(3)i
Since LHS ≠ RHS, option c) is not a root of the equation.

d) z = 1.18 - 0.43i
Substitute this value into the equation:
LHS = (1.18 - 0.43i)^2
= 0.4373 + 2.4742i
RHS = 1 - sqrt(3)i
Since LHS ≠ RHS, option d) is not a root of the equation.

Therefore, the answer is:
Option a) -0.22 + 1.24i