Simplify to get a complex number 1/(3 + 4i) in standard a + bi form.

Complex numbers are interesting types of numbers that can't be represented on the number line. A complex number has two parts: one is imaginary and the other one is real. These numbers are represented in the complex plane. They find their applications in various fields related to engineering and science.

Answer: The simplified form of the complex number 1/(3 + 4i) is 3/25 - 4/25i in the standard a + bi form.

Let's understand how did we arrive at the solution.

Explanation: 

For the given complex number 1/(3 + 4i), in order to convert it to a+bi form, let's multiply the numerator and denominator with 3 - 4i.

⇒1 / (3 + 4i) = [1 × (3 - 4i)] / [(3 + 4i) × (3 - 4i)] = 3/25 - 4/25i (simplify the denominator using the identity a² - b²)

Hence, the simplified form of the complex number 1/(3 + 4i) is 3/25 - 4/25i in the standard a + bi form.