Answer:
Step-by-step explanation:
hello :
z⁴=1+i given : z² = t t is the complex number so : z⁴= (z²)² =t²
solve for t this equation : t² = 1+i
if : t = x+iy t² =(x+iy)² = x²+2xiy+(iy)² =x²-y²+2xyi ...... ( i² = -1)
t² = 1+i means : x²-y²+2xyi = 1+i
you have this system : x²-y² = 1.....(*)
2xy = 1.....(**)
slve for x and y you ca add this equation : ....(***)
( use : t² = 1+i
/t²/ = /1+i/ so :/t/² = /1+i/ .... (√(x²+y²))²=√(1²+1²) =√2 means x²+y² = √2)
the system is : x²-y² = 1.....(*)
2xy = 1.....(**)
x²+y² = √2 ....(***)
add (*) and (***) : 2x²= 1+√2
x² = (√2+1)/2
substrac (*) and (***) you have : y² = (√2-1)/2
use (**) the proudect xy is positif (same sign) so :
x=√( (√2+1)/2) and y = √( (√2-1)/2) so : t1 =√( (√2+1)/2)+i√( (√2-1)/2)
x= -√( (√2+1)/2) and y = -√( (√2-1)/2) so :t2= -t1
same method for equation : z² =t1 ..(2 solution ) and z² = t2..(2 solution )
Please see the <em>blue</em> curve of the image attached below to know the graph of the function g(x) = (1/3) · 2ˣ.
<h3>How to graph a transformed function</h3>
Herein we have an <em>original</em> function f(x). The <em>transformed</em> function g(x) is the result of <em>compressing</em> f(x) by 1/3. Then, we find that g(x) = (1/3) · 2ˣ. Lastly, we graph both function on a <em>Cartesian</em> plane with the help of a <em>graphing</em> tool.
The result is attached below. Please notice that the <em>original</em> function f(x) is represented by the red curve, while the <em>transformed</em> function g(x) is represented by the blue curve.
To learn more on functions: brainly.com/question/12431044
#SPJ1
Answer:
The coordinates of C(22/3, 7)
Step-by-step explanation:
Partitioning between two points A and B in the ratio a:b.
The x-coordinate of the point of partition C is found at
XC = XA*(b/(a+b)+XB(a/(a+b) ..............(1)
Similarly, the x-coordinate of the point of partition is found at
YC = YA*(b/(a+b)+YB(a/(a+b)...............(2)
Given A(8,8), B(4,2), partition ratio of A:B = 1:5,
substitute in (1)
XC = 8*5/6+4*1/6 = 44/6 = 22/3
YC = 8*5/6 + 2*1/6 = 42/6 = 7
The coordinates of C(22/3, 7)
$12/25 pounds
12/25= $0.48
$0.48/pound is your answer
The answer would be A. because two negatives equal a positive