identify the standard form of the complex number: 10(cos259+isin259)
To identify the standard form of the complex number 10(cos259+isin259), we can use Euler's formula:
e^(ix) = cos(x) + isin(x)
Using this formula, we can rewrite the given complex number as:
10 * e^(i * (259))
Now, we know that e^(i * (259)) is the polar representation of the number and we need to convert it to standard form, which is in the form a + bi, where a and b are real numbers.
To convert the polar representation to standard form, we'll use Euler's formula once again:
e^(ix) = cos(x) + isin(x)
Here,
x = 259
Now, using Euler's formula, we can write the complex number in standard form:
10 * (cos(259) + isin(259))
Simplifying further:
10 * cos(259) + 10 * isin(259)
The standard form of the complex number 10(cos259 + isin259) is:
10 * cos(259) + 10 * isin(259)