# Argument problem

• Feb 1st 2011, 02:32 AM
dugongster
Argument problem
Determine the principal value of $\displaystyle (3+j4)^{1+j2}$ ?
• Feb 1st 2011, 03:13 AM
Prove It
Are you asking the find the principal argument of $\displaystyle \displaystyle (3 + j^4)^{1 + j^2}$ with $\displaystyle \displaystyle j= \sqrt{-1}$?

If not, what are $\displaystyle \displaystyle j4$ and $\displaystyle \displaystyle j2$?
• Feb 1st 2011, 03:37 AM
chisigma
$\displaystyle \displaystyle (3+j 4)^{1+j 2}= e^{(\ln 5 + j\ \tan^{-1} \frac{4}{3})\ (1+j 2)}= e^{(\ln 5 -2\ \tan^{-1} \frac{4}{3}) + j (2 \ln 5 + \tan^{-1} \frac{4}{3})}$

Kind regards

$\displaystyle \chi$ $\displaystyle \sigma$
• Feb 1st 2011, 03:42 AM
Prove It
Is it wrong to note that $\displaystyle \displaystyle 1 + j^2 = 1 - 1 = 0$,

so $\displaystyle \displaystyle (3 + j^4)^{1 + j^2} = (3 + j^4)^0 = 1 + 0i$?
• Feb 1st 2011, 04:02 AM
Plato
Quote:

Originally Posted by dugongster
Determine the principal value of $\displaystyle (3+j4)^{1+j2}$ ?

If this problem is really "Determine the principal value of" $\displaystyle (3+4i)^{1+2i}$, then that is truly a make-busy work problem.