+280 What are the solutions to x3 = −4 + 4i in polar form?
Select all correct answers below.
6√32cis(19π/12)
2 3√5cis(23π/12)
6√32cis(2π/3)
6√32cis(π/4)
2 3√5cis(7π/12)
6√32cis(11π/12)
2 3√5cis(2π/3)
2 3√5cis(5π/4)
6√32cis(4π/3)
hey! I'm not asking to do the whole problem. if someone could help me solve/find one, I can do the rest. :)
+23252 x3 = -4 + 4i
Step 1) write -4 + 4i in r·cs( theta ) form
r = sqrt( (-4)2 + (42) )
theta = tan-1( 4 / -4)
that your angle is in the second quadrant>
Step 2) To get your first answer:
take the 3rd root of the r-value and divide the angle by 3
Step 3) To find the other roots:
-- add 2pi/3 to the angle of the first answer (keep r the same)
-- add 2pi/3 to the angle of the second answer (keep r the same)
+23252 r is (32)1/2 ---> r1/3 = [ (32)1/2 ]1/3 = (32)1/6
When you find theta, you use tan-1( 4 / -4 ) = tan-1( -1 )
One of the values of tan-1( -1 ) is -45o or -pi/4 -- however --
for this problem, since the number is
-4 + 4i -- which is in the second quadrant, you need to use either:
if you are using degrees: -45o + 180o = 135o
or, if you are using radians: - pi/4 + pi = 3pi/4.
