Question

Express z 1 = − 10 3 − 10 i z 1 ​ =−10 3 ​ −10iz, start subscript, 1, end subscript, equals, minus, 10, square root of, 3, end square root, minus, 10, i in polar form. Express your answer in exact terms, using radians, where your angle is between 0 00 and 2 π 2π2, pi radians, inclusive. z 1 =

Answer 1

z = 20(cosπ/6 + isinπ/6)

Explanation:

Given the complex value

z1 = -10√3 - 10i

The polar form of the complex number is expressed as;

z = r(costheta + isintheta)

r is the modulus of the complex number

theta is the argument

r = |z1| = √x²+y²

r = √(-10√3)²+(-10)²

r = √(100(3)+100

r = √400

r = 20

theta = tan^-1(y/x)

theta = tan^-1(-10/-10√3)

theta = tan^-1(1/√3)

theta = 30°

Substitute into the polar form

z = 20(cos 30°+isin30°)

z = 20(cosπ/6 + isinπ/6)