Divide the following expression and simplify completely. Enter your answer as a complex number in standard form. (2+11i)/(3+7i) square

Question

Answer 1

To divide the complex numbers

and simplify completely, we need to multiply both the numerator and the denominator by the conjugate of the denominator. The conjugate of

is

.First, let's multiply the numerator and the denominator by the conjugate of the denominator:

Next, we perform the multiplication in the numerator and the denominator separately:### Numerator:

Using the distributive property (FOIL method):

Since

:

So the numerator becomes:

### Denominator:

Using the difference of squares formula:

Since

:

So the denominator becomes:

Now we have:

We can separate this into real and imaginary parts:

Simplifying each part:

Thus, the simplified form of the given expression is:

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