The rectangular form of the provided complex number is Z = -20√3 - 20i option (C) is correct.
What is a complex number?
It is defined as the number which can be written as x+iy where x is the real number or real part of the complex number and y is the imaginary part of the complex number and i is the iota which is nothing but a square root of -1.
We have a complex numbers in the trigonometric form:
Z = 40[cos(7π/6) + i sin(7π/6)]
As we know,
7π/6 = 7(180)/6
= 1260/6
= 210 degrees
From the trigonometric table:
cos210 = -√3/2
sin210 = -1/2
Plug the above values in the complex number:
Z = 40[-√3/2 + i (-1/2)]
Z = (40/2)[-√3 - i]
Z = 20[-√3 - i]
Z = -20√3 - 20i
Thus, the rectangular form of the provided complex number is Z = -20√3 - 20i option (C) is correct.
Learn more about the complex number here:
brainly.com/question/10251853
#SPJ5
