Complex number
Evaluate in Cartesian form: arc tan(2i)
arctan(2i) = i arctanh(2)
But that's not much help, since arctanh(x) has a domain os |x| < 1
So, fall back on the definition: arctanh(x) = 1/2 ln (1+x)/(1-x)
So now you have
arctan(2i) = i/2 ln ((1+2i)/(1-2i)) = i/2 ln(-3/5 + 4/5 i)
Now just evaluate complex logs in the normal ways.
To evaluate the complex number in Cartesian form, we need to find the value of arctan(2i).
The arctan function is typically defined for real numbers, so we need to rewrite 2i as a real number before applying the arctan function.
Let's express 2i in Cartesian form.
Recall that the standard form of a complex number is a + bi, where a and b are real numbers. In this case, since we don't have a real part, we can set a = 0 and express 2i as 0 + 2i.
Now, we can rewrite 2i as a complex number in Cartesian form: 0 + 2i.
To find the value of arctan(2i), we can apply the arctan function to the ratio of the imaginary part (2) to the real part (0).
arctan(2i) = arctan(2/0)
However, we encounter an issue because we cannot divide by zero. The complex number 2i does not have a well-defined value for the arctan function in Cartesian form.
Therefore, we cannot evaluate arctan(2i) in Cartesian form.