Compex numbers

10^(5 + 10i) * (5e^(3i))^0.5
10^5 * 10^(10i) * 5^0.5 * e^(1.5i)
223606.7977 * e^(24.52585093i)
223606.7977 * e^(5.676295008i)
223606.7977 * cos(5.676295008)+223606.7977 * sin(5.676295008) i
183676.3253-127526.4973i

Hi Peter,
I was looking at this question when your answer was posted
I also got the first 3 lines of your working but I don't see how e^(24.52585093i) becomes e^(5.676295008i)
I'd also really like to understand the next line as well.
I would be really grateful if you could explain this.
thanks.


10^(5 + 10i) * (5e^(3i))^0.5
10^5 * 10^(10i) * 5^0.5 * e^(1.5i)
223606.7977 * e^(24.52585093i)
223606.7977 * e^(5.676295008i)
223606.7977 * cos(5.676295008)+223606.7977 * sin(5.676295008) i
183676.3253-127526.4973i

e^(24.52585093i) is the direction of the value
because there is no ° at the value I know it is a radian
so you can add or sub 2π so much you want
I dicrease 2π untile the value is between 0 and 2π
You can write cos(24.52585093), too because it's the same as cos(5.676295008)

I don't know if this explaination helps, but I hope.

http://www.mhhe.com/math/precalc/barnettpc5/graphics/barnett05pcfg/ch07/others/bpc5_ch07-06.pdf (Page 557)

Thanks peter,
Your explanation helped a lot.
I got more of an explanation from the above web page and after looking at the diagram on page 557 and adding it to knowledge I already have I understood exactly.

I would like to see a proof of why e ^(i*theta) = cos(theta) + i*sin(theta)
The artical says that this relationship is shown/proved in a more advance area.

Thanks again,


Hi Baummann
Sorry I hijacked your post. Do you understand now?