# Imaginary to trig notation

• Jul 20th 2012, 07:24 AM
Greymalkin
Imaginary to trig notation
Convert (1-i)(2+2i) to trig notation and then multiply

I get:

${\sqrt{2}{(cos315+isin315)}*{\sqrt{8}{(cos45+isin4 5)}}$
$4{(cos360+isin360)}$
$4$

Book answer is: $4({cos42+isin42)$

My first part is wrong, why???

Also I have a general question other than this current problem. Why are the angles always the same in each point?
• Jul 20th 2012, 07:38 AM
a tutor
Re: Imaginary to trig notation
You're nearly right. The answer is 4i.
• Jul 20th 2012, 07:39 AM
Plato
Re: Imaginary to trig notation
Quote:

Originally Posted by Greymalkin
Convert (1+i)(2+2i) to trig notation and then multiply

I get:

${\sqrt{2}{(cos45+isin45)}*{\sqrt{8}{(cos45+isin45) }}$
$4{(cos90+isin90)}$
$4$

Book answer is: $4({cos42+isin42)$

You textbook is mistaken.
• Jul 20th 2012, 07:48 AM
Greymalkin
Re: Imaginary to trig notation
Quote:

Originally Posted by a tutor
You're nearly right. The answer is 4i.

It appears I was overhasty in posting this because I've mixed up the answers from the text, the actual answer says 4, why would you say it is 4i? isnt i*0=0?
• Jul 20th 2012, 07:53 AM
a tutor
Re: Imaginary to trig notation
Quote:

Originally Posted by Greymalkin
It appears I was overhasty in posting this because I've mixed up the answers from the text, the actual answer says 4, why would you say it is 4i? isnt i*0=0?

Because before you edited it the answer was 4i. :p
• Jul 20th 2012, 07:58 AM
Greymalkin
Re: Imaginary to trig notation
It also appears that my brain isnt into math on fridays :)
• Jul 20th 2012, 08:09 AM
ILikeSerena
Re: Imaginary to trig notation
Hmm, I do not know what you edited, but the answer should be 4i.

You seem to have deduced an angle of 315 degrees for (1+i).
But that angle should be 45 degrees.

It seems you had that before, but then you also got 4, which is still wrong - it really should be 4i.
Note that $\sin 90 = 1$.
• Jul 20th 2012, 08:17 AM
Greymalkin
Re: Imaginary to trig notation
Quote:

Originally Posted by ILikeSerena
Hmm, I do not know what you edited, but the answer should be 4i.

You seem to have deduced an angle of 315 degrees for (1+i).
But that angle should be 45 degrees.

It seems you had that before, but then you also got 4, which is still wrong - it really should be 4i.
Note that $\sin 90 = 1$.

Sorry, the real question is (1-i)(2+2i). Although my question was answered my editing was not finished, apologies.