Question

Reflect: You found that ( 3 + 4 x ) + ( 2 - x ) = 5 + 3x

Suppose x=i (the imaginary unit)
What equation do you get?
Answer must include words/explanations
(guys please help!!)

Answer 1

We start with the equation:

(3 + 4x) + (2 -x) = 5 + 3x

Now we replace:

x = i

This is just changing all the "x"s in the equation by "i"s:

(3 + 4i) + (2 - i) = 5 + 3i

This can be viewed as 3 complex numbers:

z1 = 3 + 4i

z2 = 2 - i

z3 = 5 + 3i.

Now, let's check if equality remains true:

(3 + 4i) + (2 - i) = 5 + 3i

The first step is to use the associative and commutative properties to separate the real and imaginary parts.

(3 + 2) + (4i - i)

5 + (4 - 1)*i

5 + 3i

Then the equality remains true.

And this will be true always, for anything that we feed into the x in our initial equation:

(3 + 4x) + (2 -x) = 5 + 3x

This is because x is a variable, so it can be evaluated in any number, and the equality will still be true.