Math Equation

[TheWrathOfMath]

Solve (find all solutions): (2i) ^9*z^3=(1+i) ^17, z=complex number.


When I convert to polar form and solve, I get z^3=sqrt(2)/2*cis(-45).
When I use algebric form, I get z^3=1/2-(1/2)i (which is NOT equivalent to the above polar form).

Why is that?

 

[skeeter]

[imath]\dfrac{\sqrt{2}}{2}\left[\cos(-45) + i\sin(-45)\right] = \dfrac{\sqrt{2}}{2}\left[\dfrac{\sqrt{2}}{2} + i \cdot \left(-\dfrac{\sqrt{2}}{2} \right) \right] = \dfrac{1}{2} - i \cdot \dfrac{1}{2}[/imath]

 

[Deleted member 4993]

When I convert to polar form and solve, I get z^3=sqrt(2)/2*cis(-45).

Please show us the steps - how you got to above expression.

When I use algebraic form, I get z^3=1/2-(1/2)i (which is NOT equivalent to the above polar form).

Please show us the steps - how you got to above expression.

 

[TheWrathOfMath]

Never mind. I made an asinine mistake. I already figured it out. Nevertheless, I thank you for the intention to help.

I would appreciate it if you could please assist me with the following question:

Complex Numbers Proof

Given that z and w are complex numbers whose sum is not zero, prove that [z^(1996)-w^(1996)] / (z+w) is a pure imaginary number.

www.freemathhelp.com

Please show us the steps - how you got to above expression.


Please show us the steps - how you got to above expression.

ay.

 

[topsquark]

Never mind. I made an asinine mistake. I already figured it out. Nevertheless, I thank you for the intention to help.

I would appreciate it if you could please assist me with the following question:

Complex Numbers Proof

Given that z and w are complex numbers whose sum is not zero, prove that [z^(1996)-w^(1996)] / (z+w) is a pure imaginary number.

www.freemathhelp.com

ay.

Please post this as a new thread.

-Dan

 

[Deleted member 4993]

Please post this is a new thread.

-Dan

S/he did post that as a new thread with title → complex-numbers-proof.133864/