Answer:
Step-by-step explanation:
The conjugate of a radical expression is obtained by changing the sign of the middle term.
The conjugate of 
is simply 
Therefore, to obtain the conjugate of the given expression we simply shall be changing the negative sign to positive;
The conjugate of 
is simply;
<h3>
Answer: -i</h3>
========================================================
Explanation:
i = sqrt(-1)
Lets list out the first few powers of i
- i^0 = 1
- i^1 = i
- i^2 = -1
- i^3 = i*i^2 = i*(-1) = -i
- i^4 = (i^2)^2 = (-1)^2 = 1
By the time we reach the fourth power, we repeat the cycle over again (since i^0 is also equal to 1). The cycle is of length 4, which means we'll divide the exponent over 4 to find the remainder. Ignore the quotient. That remainder will determine if we go for i^0, i^1, i^2 or i^3.
For example, i^5 = i^1 because 5/4 leads to a remainder 1.
Another example: i^6 = i^2 since 6/4 = 1 remainder 2
Again, we only care about the remainder to find out which bin we land on.
-------------
Turning to the question your teacher gave you, we have,
739/4 = 184 remainder 3
So i^739 = i^3 = -i
<h3>
-i is the final answer</h3>
--------------
Side notes:
- if i^a = i^b, then a-b is a multiple of 4
- Recall that the divisibility by 4 trick involves looking at the last two digits of the number. So i^739 is identical to i^39.
Answer:
6x - 4
Step-by-step explanation:
f(x) + g(x)
= 4x + 8 + 2x - 12 ← collect liketerms
= 6x - 4
