Find e^cos(2+3i) as a complex number expressed in cartesian form.

The complex number has Cartesian form

.

Step-by-step explanation:

First, we need to recall the definition of when is a complex number:

.

Then,

. (I)

Now, recall the definition of the complex exponential:

.

So,

(we use that .

Thus,

Now we group conveniently in the above expression:

.

Now, substituting this equality in (I) we get

.

Thus,

.

step-by-step explanation:

the original amount doesn't ''re just looking for the time it takes for 1/2 of the substance to we have

(1/2) =)     take the ln   of both sides

ln (1/2)   = )   and we can write

ln(1/2) = ) lne     and lne   = 1     so we have

ln(1/2) = -.1092t     divide both sides by -.1092

t = ln(1/2)/-.1092 = about 6.347 days = about 6.3 days (rounded)