A complex number is a number of the form a + bi where a is the real part and b is the imaginary part. Write 1/(7 + 24i) in the form of a + bi.

Complex numbers are those numbers that can't be represented on the cartesian plane or the number line. They have many applications in electrical engineering as well as many other fields of engineering.

Answer: The expression 1/(7 + 24i) can be written as 7 / 625 - 24i / 625.

Let's understand the solution in detail.

Explanation:

Given number: 1/(7 + 24i)

To represent the given number in the a + bi form, we have to multiply and divide the complex number by (7 - 24i), which is the conjugate of the number.

⇒ 1/(7 + 24i) = [1 × (7 - 24i)] / [(7 + 24i) × (7 - 24i)]

Now, using the algebraic identity x² - y² = (x - y) (x + y) and i² = -1, we have

⇒ 1 × (7 - 24i) / (7 + 24i) × (7 - 24i) = (7 - 24i) / 7² + 24² 

⇒ (7 - 24i) / 7² + 24² =7/625 - 24i/625

Hence, The expression 1/(7 + 24i) can be written as 7 / 625 - 24i / 625.