# Complex no.s raised to exponents & divided...

• Sep 12th 2012, 05:39 AM
Toyboy
Complex no.s raised to exponents & divided...
Hi guys,

i have a problem...it goes like this:

Given: z1= 2,5+8i and z2= 0,5-3i

2) Now Calculate: (z1)^2/(z2)^3

This is what my answer looks like: -947,969/874,704 - 1309,438i/874,704

I need to know where i went wrong please?

• Sep 12th 2012, 06:13 AM
Wilmer
Re: Complex no.s raised to exponents & divided...
Quote:

Originally Posted by Toyboy
Given: z1= 2,5+8i and z2= 0,5-3i

Now Calculate: (z1)^2/(z2)^3

This is what my answer looks like: -947,969/874,704 - 1309,438i/874,704

I need to know where i went wrong please?

Well, (5/2 + 8i)^2 = (160i - 231) / 4
and (1/2 - 3i)^3 = (198i - 107) / 8
SO:
[(160i - 231) / 4] / [(198i - 107) / 8] = (320i - 462) / (198i - 107)

Hope that helps...
• Sep 12th 2012, 06:50 AM
HallsofIvy
Re: Complex no.s raised to exponents & divided...
But since you don't tell us what you did there is no way to say what, if anything, you did wrong!
• Sep 12th 2012, 06:56 AM
Toyboy
Re: Complex no.s raised to exponents & divided...
Quote:

Originally Posted by HallsofIvy
But since you don't tell us what you did there is no way to say what, if anything, you did wrong!

My apologies, this is what i did:

(2,5+8i)^2/(0,5-3i)^3
(2,5+8i)(2,5+8i)/(0,5-3i)(0,5-3i)(0,5-3i)

....mulitplied it all out and ended up with this: -947,969/874,704 - 1309,438i/874,704
• Sep 12th 2012, 07:18 AM
Wilmer
Re: Complex no.s raised to exponents & divided...
Quote:

Originally Posted by Toyboy
(2,5+8i)(2,5+8i)

Do you get what I got when you complete that one...see my previous post... ??
• Sep 12th 2012, 07:26 AM
Toyboy
Re: Complex no.s raised to exponents & divided...
Quote:

Originally Posted by Wilmer
Do you get what I got when you complete that one...see my previous post... ??

Nope, it does not, mine equates to -1.084-1.497i
• Sep 12th 2012, 08:04 AM
Wilmer
Re: Complex no.s raised to exponents & divided...
Sorry, but got no idea what you're talking about or doing...
mine equates to -57.75 + 40i ; or to -17.75 if 1 is used instead of i

I get: (2.5 + 8i)^2 = (160i - 231) / 4
What do you get: (2.5 + 8i)^2 = ?
• Sep 12th 2012, 08:51 AM
MaxJasper
Re: Complex no.s raised to exponents & divided...
Quote:

Originally Posted by Toyboy
Given: z1= 2,5+8i and z2= 0,5-3i
2) Now Calculate: (z1)^2/(z2)^3
This is what my answer looks like: -947,969/874,704 - 1309,438i/874,704

$\displaystyle \frac{{z1}^2}{{z2}^3}=2.22 +1.13 i$
• Sep 12th 2012, 09:18 AM
Wilmer
Re: Complex no.s raised to exponents & divided...
Quote:

Originally Posted by MaxJasper
$\displaystyle \frac{{z1}^2}{{z2}^3}=2.22 +1.13 i$

Agree. (320i - 462) / (198i - 107) = ~2.226798 + ~1.129962 i