How do you divide a complex number by an integer?

Dividing a complex number by an integer is achieved by dividing both the real and imaginary parts of the complex number by the integer.

Here's a breakdown:

Suppose you have a complex number in the form a + bi, where a and b are real numbers, and i is the imaginary unit (√-1). If you want to divide this complex number by an integer n, you perform the following operation:

(a + bi) / n = (a/n) + (b/n)i

Essentially, you're distributing the division over both the real and imaginary parts.

Example

Let's say you want to divide the complex number 6 + 4i by the integer 2.

(6 + 4i) / 2 = (6/2) + (4/2)i = 3 + 2i

So, the result of dividing 6 + 4i by 2 is 3 + 2i.

Steps

1. Identify the complex number: Express it in the form a + bi.
2. Identify the integer: This is the number you're dividing by (n).
3. Divide the real part: Divide 'a' by 'n'.
4. Divide the imaginary part: Divide 'b' by 'n'.
5. Combine the results: The result is (a/n) + (b/n)i.

Note

The provided reference discusses dividing a complex number by another complex number (specifically one with an imaginary component in the denominator) and involves multiplying by the conjugate to eliminate the imaginary part from the denominator. However, this is a different operation than dividing a complex number by an integer.