1. ## Complex equations

Hi!

I got stuck on these 2 questions when I tried to do some math:

A)

IF its possible solve the equation:

z− 4iz= 3 + i

B)

Write the complex number z in polar form and the form eZ. Reply to this in precise form.
 z= 2 + 2i Thx for any help!

2. ## Re: Complex equations

Originally Posted by Aiyla
A)
[TR]
[TD]z− 4iz= 3 + [I]i
Use $z=x+yi$ transform to $(x+4y)+(-4x+y)i=3+i$.
So solve $(x+4y)=3~\&~(-4x+y)=1$

3. ## Re: Complex equations

Thx for the help but I am totally lost how do I solve (x+4y)=3 and (-4x+y)=1 ?

4. ## Re: Complex equations

Originally Posted by Aiyla
Thx for the help but I am totally lost how do I solve (x+4y)=3 and (-4x+y)=1 ?
$x+yi=a+bi\text{ if and only if }x=a~\&~y=b$
That is a system of two equations in two unknowns.

5. ## Re: Complex equations

??? Still don't get it,sorry...

6. ## Re: Complex equations

Originally Posted by Aiyla
??? Still don't get it,sorry...
Can you solve this system:
\begin{align*}x+4y&=3 \\-4x+y&=1\end{align*}~~?

If not you need to review basic basic algebra.

7. ## Re: Complex equations

is the answer 13x + y = 3 ?

8. ## Re: Complex equations

Originally Posted by Aiyla
is the answer 13x + y = 3 ?
You are not ready to work this problem.
You need a good review of beginning algebra.
This material should have been learned in middle school.

9. ## Re: Complex equations

Could you explain what the answer will be then just so I can understand?

10. ## Re: Complex equations

Originally Posted by Aiyla
??? Still don't get it,sorry...
This is a system of linear equations. You definitely should have learned how to solve these in an earlier algebra class.

We have

$\begin{array}{rcrcr}x & + & 4y & = & 3\\-4x & + & y & = & 1\end{array}$

Multiply the first equation by 4:

$\begin{array}{rcrcr}4x & + & 16y & = & 12\\-4x & + & y & = & 1\end{array}$

Add the first equation to the second:

$\begin{array}{rcrcr}4x & + & 16y & = & 12\\&& 17y & = & 13\end{array}$

So $y = \frac{13}{17}$. Substitute this into the first equation and solve for $x$.

Originally Posted by Aiyla
Write the complex number z in polar form and the form eZ. Reply to this in precise form.
z=2+2i
Start by finding the modulus and argument of $z$. Consult your textbook if necessary.

11. ## Re: Complex equations

Originally Posted by Aiyla
Could you explain what the answer will be then just so I can understand?
This is not a tutorial service.
You can find tutorial services in the web, but be prepared to pay.
We are a free help service. But helping is different from tutoring.

12. ## Re: Complex equations

x= -1/17

There, thx for the help!

13. ## Re: Complex equations

Originally Posted by Aiyla
x= -1/17
Right. So then what does $z$ equal?