<span>use De Moivre's Theorem:
⁵√[243(cos 260° + i sin 260°)] = [243(cos 260° + i sin 260°)]^(1/5)
= 243^(1/5) (cos (260 / 5)° + i sin (260 / 5)°)
= 3 (cos 52° + i sin 52°)
z1 = 3 (cos 52° + i sin 52°) ←← so that's the first root
there are 5 roots so the angle between each root is 360/5 = 72°
then the other four roots are:
z2 = 3 (cos (52 + 72)° + i sin (52+ 72)°) = 3 (cos 124° + i sin 124°)
z3 = 3 (cos (124 + 72)° + i sin (124 + 72)°) = 3 (cos 196° + i sin 196°)
z4 = 3 (cos (196 + 72)² + i sin (196 + 72)°) = 3 (cos 268° + i sin 268°)
z5 = 3 (cos (268 + 72)° + i sin (268 + 72)°) = 3 (cos 340° + i sin 340°) </span>
Answer:
y= -1/2x + 3
Step-by-step explanation:
A line perpendicular will have the reciprocal slope.
First you need to find the slope of the line given.
m= rise/ run
m= -2
Now flip for the reciprocal.
The perpendicular line will have a slope of -1/2
Answer:
let me take a guess and if its wrong sorry
Step-by-step explanation:
12
Answer:
Rule:
Step-by-step explanation:
<em>I will answer generally, since the coordinates of f, g and h are not given</em>
Given
Point: x, y
Translation Rule
1 : x + 3, y - 1
2: 90 degree counterclockwise
Required
Determine the new coordinates
<u>At the first translation of (x,y) by x + 3, y - 1</u>
The new point is: 
<u>At the second translation (90 degrees counterclockwise)</u>
When a point (x,y) is translated using this rule, it becomes (-y,x)
So, the new point is:
If the initial point of h is (2,3),
The new point is:
Answer:
○ 4⁄6, -4⁄6
Step-by-step explanation:
Take the square root of both the denominator and numerator, and you will get the above two answers.
I am joyous to assist you anytime.
