We have an arithmetic progression:
Nth=an
an=a₁+(n-1)d
a₁ is the first term.
n=number of terms.
d=common difference
10,17,24,31...
a₁=10
d=a₂-a₁=17-10=7
Therefore:
Nth=an
an=a₁+(n-1)d
an=10+(n-1)7
an=10+7n-7
an=7n+3.
Therefore: the formula for the nth is, an=a+(n-1), in this case; an=7n+3,
To check:
a₁=7*1+3=10
a₂=7*2+3=17
a₃=7*3+3=24
a₄=7*4+3=31
a₅=7*5+3=38.......
6i/ (1+i)
multiply by the complex conjugate (1-i)/(1-i)
6i/(1+i) * (1-i)/(1-i)
6i* (1-i) = 6i - 6i^2 = 6i - 6(-1) = 6i +6
(1+i)*(1-i)= 1-i +i -i^2 = 1 -i+i -(-1) = 1+1=2
(6+6i)/2
3+3i
Answer: 3+3i
Let's analyse the function

The amplitude is A, so we want A=1.5
Now, we start at x=0, and we have 
After one second, i.e. x=1, we want this sine function to make 330 cycles, i.e. the argument must be 
So, we have

so, the function is

Answer:
Option A and Option B are not equivalent to the given expression.
Step-by-step explanation:
We are given the following expression:

Applying properties of exponents and base:

A. Using the exponential property
, we can write:

which is not equal to the given expression.
B. Using the exponential property
, we can write:

which is not equal to the given expression.
C. First we convert the radical form into exponent form. Then by using the property
of exponent, we can write the following:

which is equal to the given expression.
D. First we convert the radical form into exponent form. Then by using the property
of exponent, we can write the following:

which is equal to the given expression.
Option D and Option C are equivalent to the given expression.