Write the following roots in standard form.(Round your answer to four decimal places.)
Cube roots of
A)
B)
C)
D)

Question

Write the following roots in standard form.(Round your answer to four decimal places.) ​
Cube roots of  ​
A) ​ 
B) ​ 
C) ​ 
D) ​

Quizplus · Accepted Answer

The standard form of a cube root of a number in the form a + bi is: 
cuberoot(a + bi) = m(cuberoot(a^2 + b^2))(cos(theta/3) + i(sin(theta/3))) 
where m = cuberoot of (a^2 + b^2), and theta = arg(a + bi) 
Using this formula on all given roots, 
A) 2.2371(cuberoot(11))(cos(322.756/3) + i(sin(322.756/3))) 
B) 2.2371(cuberoot(11))(cos(323.117/3) + i(sin(323.117/3))) 
C) 2.2371(cuberoot(11))(cos(323.118/3) + i(sin(323.118/3))) 
D) 2.2371(cuberoot(11))(cos(323.376/3) + i(sin(323.376/3))) 
E) 2.2371(cuberoot(11))(cos(323.377/3) + i(sin(323.377/3))) 
Round to four decimal places, the only root in standard form is E with a real part of 1.2469 and an imaginary part of 2.1547.

Write the Following Roots in Standard Form