+79 What are the fourth roots of \(-3+3\sqrt{3}i\)?
Enter your answer by filling in the boxes. Enter the roots in order of increasing angle measure in the simplest form.
4 answers in form:
___cis(___)
+23245 To find the primary fourth root of the complex number a + b·i, place the number into r·cis( theta ) form.
r = sqrt( a2 + b2 )
theta = tan-1( b/a ) [make certain that the angle is in the correct quadrant; in this case, the 2nd[
The primary fourth root will be: r1/4·cis( theta/4 ).
To find the other three roots, change the angle by adding pi/2, pi, and 3pi/2 to the original angle.
