# Thread: Argument of complex number

1. ## Argument of complex number

"Compute Arg(1+2i) x Arg(2+3i)"

So:

$\displaystyle (1+2i)x(2+3i)$

$\displaystyle 2+7i-6$

$\displaystyle -4+7i$

$\displaystyle Tan = 7/-4$

$\displaystyle Tan-1= 7 / -4$

I keep getting -60 degrees, but it should be something like 100 degrees. What am I doing wrong?

2. Originally Posted by coasterguy
"Compute Arg(1+2i) x Arg(2+3i)"

Mr F asks: Is this meant to be a product of arguments? Or are you trying to find the arument of (1 + 2i)(2 + 3i)? Your 'solution' suggests the latter.

So:

$\displaystyle (1+2i)x(2+3i)$

$\displaystyle 2+7i-6$

$\displaystyle -4+7i$

$\displaystyle Tan = 7/-4$

$\displaystyle Tan-1= 7 / -4$

I keep getting -60 degrees, but it should be something like 100 degrees. What am I doing wrong?
-4 + 7i lies in the second quadrant. So you want the angle $\displaystyle \alpha$ lying in the second quadrant such that $\displaystyle \tan \alpha = - \frac{7}{4}$. It is not a 'special angle' so you will have to use your calculator and get a decimal approximation.

But this is not the answer to the question as posted. The answer to the question you've posted is $\displaystyle \tan^{-1} (2) \cdot \tan^{-1} \left( \frac{3}{2} \right)$.