Hello.

Complex number is given: $\LARGE z=3-4i$ solve: $\LARGE w=|z|+2i$

I thought about...
$\LARGE w=|z|+2i$
$\LARGE w-2i=|z|$

$\LARGE |z|=w-2i$

Now I took two cases...

$\LARGE |3-4i|=w-2i\quad \quad \quad \LARGE |3-4i|=-(w-2i)$

$\LARGE 3-4i=w-2i\quad \quad \quad \LARGE 3-4i=-w+2i$

$\LARGE 3-2i=w\quad \quad \quad \LARGE 3-6i=-w$

$\LARGE 3-2i=w\quad \quad \quad \LARGE 6i-3=w$

but multiple choices are...

$\LARGE w=4-2i$

$\LARGE w=5+2i$

$\LARGE w=6+4i$

$\LARGE w=7-4i$

and I need help here.. Thank you.

Question

Hello.

Complex number is given: $\LARGE z=3-4i$  solve: $\LARGE w=|z|+2i$

I thought about...
$\LARGE w=|z|+2i$
$\LARGE w-2i=|z|$

$\LARGE |z|=w-2i$

Now I took two cases... 

$\LARGE |3-4i|=w-2i\quad \quad \quad   \LARGE |3-4i|=-(w-2i)$ 

$\LARGE 3-4i=w-2i\quad \quad \quad   \LARGE 3-4i=-w+2i$
 
$\LARGE 3-2i=w\quad \quad \quad   \LARGE 3-6i=-w$ 

$\LARGE 3-2i=w\quad \quad \quad   \LARGE 6i-3=w$ 

but multiple  choices are...


$\LARGE w=4-2i$

$\LARGE w=5+2i$

$\LARGE w=6+4i$

$\LARGE w=7-4i$

and I need help here.. Thank you.

anonymous · Answer

@Kreshnik 

|z| = |x + iy| = sqrt ( x^2 + y^2)

anonymous · Answer

huh?  :A ....  ok thanks. I'll try that :(

anonymous · Answer

Now you should get your answer :D

anonymous · Answer

thank you :D

anonymous · Answer

it's B... lol

anonymous · Answer

yw :)