Imaginary to trig notation

Convert (1-i)(2+2i) to trig notation and then multiply

__I get:__

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

$\displaystyle 4{(cos360+isin360)}$

$\displaystyle 4$

__Book answer is:__ $\displaystyle 4({cos42+isin42)$

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?

Re: Imaginary to trig notation

You're nearly right. The answer is 4i.

Re: Imaginary to trig notation

Quote:

Originally Posted by

**Greymalkin** Convert (1+i)(2+2i) to trig notation and then multiply

__I get:__

$\displaystyle {\sqrt{2}{(cos45+isin45)}*{\sqrt{8}{(cos45+isin45) }}$

$\displaystyle 4{(cos90+isin90)}$

$\displaystyle 4$

__Book answer is:__ $\displaystyle 4({cos42+isin42)$

You textbook is mistaken.

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?

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

Re: Imaginary to trig notation

It also appears that my brain isnt into math on fridays :)

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 $\displaystyle \sin 90 = 1$.

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 $\displaystyle \sin 90 = 1$.

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