# Two complex number problems!

• Nov 29th 2009, 04:38 PM
TheJoker
Two complex number problems!
Because it's my first post on this forum, I would like to thank everyone who contributed to create such a wonderful forum.

I have to solve this two problems:

1. Find $\displaystyle Re(z)=?$ $\displaystyle Im(z)=?$

if:

$\displaystyle z=\sqrt[3]{\frac{2}{-\sqrt{2+i\sqrt{2}}}}$

For first problem i don't have a clue how to come to a solution.

2. Find $\displaystyle |z+1|+z+i=0$

I know that $\displaystyle |Z|=\sqrt{x^2+y^2}$ but, what is $\displaystyle |z+1|$?

Thank you very much and sorry for my english.
• Nov 29th 2009, 04:57 PM
Chris L T521
Quote:

Originally Posted by TheJoker
Because it's my first post on this forum, I would like to thank everyone who contributed to create such a wonderful forum.

I have to solve this two problems:

1. Find $\displaystyle Re(z)=?$ $\displaystyle Im(z)=?$

if:

$\displaystyle z=\sqrt[3]{\frac{2}{-\sqrt{2+i\sqrt{2}}}}$

For first problem i don't have a clue how to come to a solution.

I think you're missing something in this problem...should something be in front of the minus sign?

Quote:

2. Find $\displaystyle |z+1|+z+i=0$

I know that $\displaystyle |Z|=\sqrt{x^2+y^2}$ but, what is $\displaystyle |z+1|$?

Thank you very much and sorry for my english.
$\displaystyle \left|z+1\right|=\left|(x+1)+iy\right|=\sqrt{(x+1) ^2+y^2}$

From there, you'll get the system of equations (after comparing real and complex coefficients):

$\displaystyle \left\{\begin{array}{l}x^2+3x+1+y^2=0\\ y=-1\end{array}\right.$

Then solve the system (you'll get two solutions).
• Nov 30th 2009, 12:29 AM
TheJoker
Hi Chris,

I rechecked the first problem and I'm not missing anything. It's OK.

Thank you for second solution.
• Nov 30th 2009, 02:38 AM
HallsofIvy
Quote:

Originally Posted by TheJoker
Because it's my first post on this forum, I would like to thank everyone who contributed to create such a wonderful forum.

I have to solve this two problems:

1. Find $\displaystyle Re(z)=?$ $\displaystyle Im(z)=?$

if:

$\displaystyle z=\sqrt[3]{\frac{2}{-\sqrt{2+i\sqrt{2}}}}$
For first problem i don't have a clue how to come to a solution.

$\displaystyle z^3= -\frac{2}{2+i\sqrt{3}}$
$\displaystyle z^3= -\frac{4+ 2i\sqrt{3}}{7}$
Write that in "polar form" with r= $\displaystyle \frac{2\sqrt{5}}{7}$, $\displaystyle \theta= 0.227\pi$ and use DeMoivre's formula to solve for z.

Quote:

2. Find $\displaystyle |z+1|+z+i=0$

I know that $\displaystyle |Z|=\sqrt{x^2+y^2}$ but, what is $\displaystyle |z+1|$?

Thank you very much and sorry for my english.
Let z= a+ bi. Then $\displaystyle |z+1|= |a+1+ bi|= \sqrt{(a+1)^2+ b^2}$

Your English is excellent. Far better than my (put language of your choice here)!
• Dec 2nd 2009, 11:49 AM
TheJoker
Thank you very much HallsofIvy.