How do I write a complex and replace it with different equations with trigonometry signs and return it back to the main function

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C

1. Define a C structure complx for a complex number with two data
members for the (real, imaginary) of the complex number. It should handle any real numbers! Use typedef to make your program readable.
2.write a procedure to raise any complex number to any integer power (𝑥 + 𝑗𝑦)^n
Where 𝑥 and 𝑦 are real number and 𝑛 is an integer!
3.write (𝑥 + 𝑗𝑦)𝑎𝑠 𝑅e^𝑗𝜃 where 𝑅 = √(𝑥^2 + 𝑦^2) 𝑎𝑛𝑑 tan^−1(𝜃) = (𝑦/𝑥)
4. Then write (𝑥 + 𝑗𝑦)^𝑛 𝑎𝑠 𝑅^𝑛*𝑒^𝑗𝑛𝜃 and go back to write the result as 𝑅^𝑛*𝑒^𝑗𝑛𝜃 𝑎𝑠 (𝑅^𝑛*𝑐𝑜𝑠(𝑛𝜃) + 𝑗𝑅^𝑛*𝑠𝑖𝑛(𝑛𝜃))
5. In your procedure (function) you will use for-loop to compute the value
of 𝑅^𝑛. Write programs to compute the 𝑠𝑖𝑛(𝑥) 𝑎𝑛𝑑 𝑐𝑜𝑠(𝑥) functions. You may
use the math library header file and use the trig functions
[𝑠𝑖𝑛( ) , 𝑐𝑜𝑠( ) 𝑎𝑛𝑑 𝑡𝑎𝑛( )] and the square-root functions only!
6. Note that the 𝑡𝑎𝑛(𝑥) is multi-valued. check if it is in the fourth quadrant
7. The function should print the result on the screen in the form
Ans: ( x, jy)and return the function to main()

What I have tried:

#include<complex.h>
#include<mathlib.h>
typedef struct complex
{
float real,imag;
}
int main()
{