exact value of e^2x=-3

Question

anonymous · Answer

check your question.

noelgreco · Answer

Your exponential is not going to be non-positive.

Forgive the double negative.

anonymous · Answer

$$-3=e^{\log_e(-3)}=e^{\ln-3}$$

anonymous · Answer

e^2x cannot equal a negative number

anonymous · Answer

Complex numbers

anonymous · Answer

i just looked at the answer in the back of the book and it says no solution your all right but how this is concluded i don't know, if anyone would like to shed some light on this please go ahead

anonymous · Answer

$$e^{2x}=-3$$
$$e^{iy}=cosy+isiny$$
Call x=iy
$$e^{i2y}=-3$$
The imaginary part of
$$e^{i2y}=0$$
Therfore
$$siny=0$$
Thus$$y=\pi n$$

anonymous · Answer

$$x=i\pi n$$

anonymous · Answer

Okay, I'll give an overview of complex no.s

anonymous · Answer

http://betterexplained.com/articles/a-visual-intuitive-guide-to-imaginary-numbers/ http://www.youtube.com/watch?v=2aQ1s1ioNWM and for e^iy=.... http://www.youtube.com/watch?v=qpOj98VNJi4

anonymous · Answer

you can help me with Iny = 13x if you want

anonymous · Answer

But to sum up- 
- Multiplying= scaling numbers
- Multiplying by negative= scaling & flipping 180 degrees on the number line
|dw:1346673982042:dw|
So, it's almost as if when numbers multiply, they 'add' their 'angles', but positive numbers have 0 degrees, and negatives, 180

What squares to -1? -1 'has' 180 degrees if you measure 0 degrees as a number pointing rightwards on a number line.
This question is the same as 'what angle adds twice to make 180?' obviously, 90 (or -90).

So there is a number with '90 degrees', the square root of -1, which we call i. I can scale also, like normal negative numbers, so you can have 6i, 0.5i etc.|dw:1346674007860:dw|