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 )
Lets solve for x.
0.8x = 50. - Remember that the jacket was 80% of the original price.
Thus, divide by x.
x = 50 / 0.8
x = 62.5
Email the teacher and see if she can check it at a later time
Combine like terms:
-12 + 5a - a - 6a + 8a + 8 + 3a
5a - a = 4a
4a - 6a = -2a
-2a + 8a = 6a
6a + 3a = 9a
-12 + 8 = -4
Answer
Answer:
V= 1767.2
Step-by-step explanation:
V=4/3πr3
(I'm pretty sure I rounded that right. If not it's 1767.15 before rounding. )
