help for complex numbers question (1 Viewer)

[english? ensquish]

Hi, I'm stuck on this question and would like help. Thanks if anyone can explain.

 

[5uckerberg]

Hi, I'm stuck on this question and would like help. Thanks if anyone can explain.

View attachment 37310

Step 1 Draw an Argand diagram with the complex number specified
Step 2 Write in mod-arg form.
Step 3 Rewrite step 2 but instead modify the mod-arg form so that it looks like this where n is an integer
Step 4 Since this is cube root we divide the angle by 3 which is a reversal of De Moivre's Theorem and cube root the 2 giving us
Step 5 All the cube roots have to be within the domain of so using what we know we will then have these three answers
Step 6 Put them on the Argand diagram
Step 7 Use Pythagoras Theorem and trigonometry in conjunction with the area of the triangle to solve the problem.

 

[Drongoski]

Area: ??

 

[5uckerberg]

Area: ??

That would be correct if the question was find three cube roots of the complex number but instead the answer is

 

[Drongoski]

That would be correct if the question was find three cube roots of the complex number but instead the answer is

Oh ya! I mistakenly used 2 as the radius of the corresponding circle instead of the cube-root of 2. Thanks.