Question

If 23 - 3 = a + b√3, and 3 + 3i, find the values f a and b, respectively.

a. 5/2, 3/2
b. 2/5, -3/2
c. 4/3, 3/2
d. -5/2, 3/2

Answer 1

The values of a and b are 20 and 0, respectively.

Step-by-step explanation:

In this problem, we are asked to find the values of a and b given the equation 23 - 3 = a + b√3 and the complex number 3 + 3i.

We can start by solving the equation 23 - 3 = a + b√3 to find the values of a and b.

23 - 3 = a + b√3
20 = a + b√3

Since the complex number 3 + 3i can be written as 3 + 3√(-1), we can substitute these values into the equation:

20 = a + b√3
20 = a + b(3√(-1))

Now we can equate the real and imaginary parts of the equation:

a = 20
b(3√(-1)) = 0

Solving for b, we find that b = 0. Therefore, the values of a and b are 20 and 0, respectively.