# Calculate the complex expression and display the solutions in the complex plane.

#### Erros

##### New member
Hello everyone, I know that maybe it should be done using the sine and cosine formula for complex numbers and to determine the modulus of this expression... but I'm not sure, it's very urgent and important for me, so can someone help me how to do it and explain it... I need Calculate the expression and display the solutions in the complex plane.

Last edited:

#### Steven G

##### Elite Member
What are you trying to solve??? You never stated what you wanted to do with this expression!

Do you want to know what you get if you add 7 to it or if you square it or if you divide by 12-4i or .....

D

#### Deleted member 4993

##### Guest
Hello everyone, I know that maybe it should be done using the sine and cosine formula for complex numbers and to determine the modulus of this expression... but I'm not sure, it's very urgent and important for me, so can someone help me how to do it and explain it...View attachment 34171

View attachment 34172
You have NOT stated:

What is the task? - "solve" does not make sense - because you do not have an "equation" containing "=" sign.

#### Erros

##### New member
What are you trying to solve??? You never stated what you wanted to do with this expression!

Do you want to know what you get if you add 7 to it or if you square it or if you divide by 12-4i or .....
Calculate the expression and display the solutions in the complex plane.

#### Erros

##### New member
You have NOT stated:

What is the task? - "solve" does not make sense - because you do not have an "equation" containing "=" sign.
Sorry my mistake, i will edit

#### Steven G

##### Elite Member
Use sines and cosines as you stated in your OP.

D

#### Deleted member 4993

##### Guest
Calculate the expression and display the solutions in the complex plane.
Are you trying to display the "given expression" as

r * [$$\displaystyle cos(\theta) + i * sin(\theta)]$$​

#### Dr.Peterson

##### Elite Member
View attachment 34173 I have done this now, what do I need next?
Where do [imath]\sqrt[6]{2}[/imath] and [imath]\frac{5\pi}{36}[/imath] come from? Are you taking the 6th root, instead of the 4th as stated in the problem? Please show your work, not just your answer.

#### Erros

##### New member
I uploaded the wrong image sry moment.
Odakle dolaze [imath]\sqrt[6]{2}[/imath] i [imath]\frac{5\pi}{36}[/imath]? Uzimate li 6. korijen, umjesto 4. kako je navedeno u problemu? Pokažite svoj rad, a ne samo svoj odgovor.

What is next ?

#### pka

##### Elite Member
Hello everyone, I know that maybe it should be done using the sine and cosine formula for complex numbers and to determine the modulus of this expression... but I'm not sure, it's very urgent and important for me, so can someone help me how to do it and explain it... I need Calculate the expression and display the solutions in the complex plane.View attachment 34171

View attachment 34172
If [imath]z=a+b\bf i[/imath] where [imath]a<0~\&~b>0[/imath] as in this case then the argument is [imath]\arg(z)=\pi+\arctan\left(\dfrac{b}{a}\right)[/imath]
Therefore here [imath]-1+\sqrt{3}{\bf{i}}=2\exp\left(\dfrac{\pi i}{3}\right)[/imath].
Thus what is [imath]\sqrt[4]{-1+\sqrt{3}{\bf{i}}}~?[/imath]