Can you tell me if my answers are correct for these problems?
1. 3i - 10
---------
8i - 5
Answer 74 65i
---- + -----
89 89
2. 11i^2 + 1
-----------
-12i - 8
Answer: 5 (2 - 3 i)
-------------
26
3. square root -25 * 8 square root -49
Answer: -280
4. square root -64 + 12 square root -36
Answer: 80 i
5. square root -13 - 6 square root -13
Answer: -5 i square root 13
(sorry this formatted weirdly, it's meant to be this if you can't tell)
1. 3i - 10 over 8i - 5
Answer: 74 over 89 + 65 i over 89
2. 11i^2 + 1 over -12i - 8
Answer: 5 (2 - 3 i) over 26
To check if your answers are correct, we will work through each problem step by step.
1. Simplify the expression (3i - 10) / (8i - 5):
To do this, multiply both the numerator and denominator by the complex conjugate of the denominator (8i + 5). The complex conjugate of a complex number a + bi is a - bi.
(3i - 10)*(8i + 5) = 74 + 65i
------------------------- = ---------------
(8i - 5)*(8i + 5) = 89
So, the simplified answer is 74 + 65i
-----
89
Your answer is correct!
2. Simplify the expression (11i^2 + 1) / (-12i - 8):
Since i^2 is defined as -1, we can substitute -1 for i^2:
(11*(-1) + 1) = -10
--------------
(-12i - 8)
Simplifying further, we can factor -2 out of the numerator:
-2*(5 - 1i)
-----------
(-12i - 8)
Now we can simplify the expression:
-2*(5 - 1i) 5 - 1i
----------- = ---------------
(-12)*(-2) 26
So, the simplified answer is (5 - i) / 13.
----
26
Your answer is incorrect.
3. Solve the expression sqrt(-25) * 8 * sqrt(-49):
First, let's simplify the square roots:
sqrt(-25) = 5i
sqrt(-49) = 7i
Now we multiply:
5i * 8 * 7i = 40i^2 * 7 = 40*(-1)*7 = -280
So, the answer is -280.
Your answer is correct!
4. Solve the expression sqrt(-64) + 12 * sqrt(-36):
First, let's simplify the square roots:
sqrt(-64) = 8i
sqrt(-36) = 6i
Now we add the terms:
8i + 12 * 6i = 8i + 72i = 80i
So, the answer is 80i.
Your answer is correct!
5. Solve the expression sqrt(-13) - 6 * sqrt(-13):
First, let's simplify the square roots:
sqrt(-13) = sqrt(13)i
Now we subtract the terms:
sqrt(13)i - 6 * sqrt(13)i = (1 - 6)sqrt(13)i = -5 sqrt(13)i
So, the answer is -5 sqrt(13)i.
Your answer is correct!
Overall, 4 out of the 5 answers are correct. Great job!