Hi, can anyone show me how to do this problem? 100 points for this.
Thanks in advance
2 answers:
Answer:
z^2 + (-1 + 5·i)·z + 14 - 7·i = 0
(1 + 2·i)^2 + (-1 + 5·i)·(1 + 2·i) + 14 - 7·i = 0
(1 + 4·i - 4) + (-1 - 2·i + 5·i - 10) + 14 - 7·i = 0
0 = 0 --> true
z^2 + (-1 + 5·i)·z + 14 - 7·i = 0
(1 - 2·i)^2 + (-1 + 5·i)·(1 - 2·i) + 14 - 7·i = 0
(1 - 4·i - 4) + (-1 + 2·i + 5·i + 10) + 14 - 7·i = 0
20 - 4·i = 0 --> false
z^2 + (-1 + 5·i)·z + 14 - 7·i = 0
1+2i is a root
z= 1+2i
z^2 = (1+2i) (1+2i)
= 1 +2i+2i +4i^2
= 1 +4i -4
= -3+4i
= (-1+5i) (1+2i)
-1+5i-2i+10i^2
-1+3i-10
-11+3i
z^2 + (-1 + 5·i)·z + 14 - 7·i = 0
-3+4i + -11+3i +14 - 7i
Combine like terms
-3-11 +14 +4i +3i-7i
0
So 1+2i is a root
1-2i is not a root
z= 1-2i
z^2 = (1-2i) (1-2i)
= 1 -2i-2i +4i^2
= 1 -4i -4
= -3-4i
= (-1+5i) (1-2i)
-1+5i+2i-10i^2
-1+7i+10
9+7i
z^2 + (-1 + 5·i)·z + 14 - 7·i = 0
-3-4i + 9+7i +14 - 7i
Combine like terms
-3+9 +14 -4i +7i-7i
20 -4i
So 1-2i is not a root
The complex conjugate being roots is only true for real coefficients
You might be interested in
Answer:
20
Step-by-step explanation:
7x - 5 = 0
7x = 5
x = 5/7
--------------------------
<h3>Answer:</h3>
1/120
<h3>Explanation:</h3>
The numerator of the probability fraction will be the number of ways to arrange 3 items: 3! = 6. So the probability fraction is ...
... 6/720 = 1/120
_____
The 3 items are the three married couples with the woman on the left.
Answer:
(5)
Step-by-step explanation:
The given two points are:
A(3,k) and B(h,4)
Now, using the distance formula that is=
.
In the given points,
,
,
and
, thus,
=
which is the required equation, hence option 5 is correct.