Step 1
I would write it as:
Then I will use the conversion from expoential to trigonometric form of a complex number as:
with in radians:
and convert it into rectangular form getting:
Vasquez
Expert2022-01-18Added 669 answers
Step 1
Given the expression of the exponential function
1)
We are asked to convert this exponential function given in the equation (1) in the form
a complex number
Firstly, we write the exponential function as follows
2)
Now we covert the exponential function to trigonometric form of a complex number.
This is done by using the Euler’s formula which is given by
Where, base of the natural logarithmic function
imaginary unit
angle in radians
In the exponential function , we have
Hence by Euler’s formula we get,
3)
Now we substitute the expression of given in the equation (3) in the equation (2), we get,
4)
Now we calculate the values of each term in the R.H.S. using the calculator.
For we obtain the value as,
For we obtain the value as,
For we obtain the value as,
Substituting all this values in the equation (4) we get,