The complex number given is 4i. To find the complex conjugate and the modulus, let’s break this down into two parts.
Complex Conjugate:
The complex conjugate of a complex number a + bi is a – bi. In our case, the number 4i can be rewritten as 0 + 4i, where a = 0 and b = 4. Therefore, the complex conjugate of 4i is 0 – 4i or simply -4i.
Modulus:
The modulus of a complex number a + bi is calculated using the formula √(a² + b²). For 4i, we again rewrite it as 0 + 4i, which gives us a = 0 and b = 4. Substituting these values into the modulus formula, we get:
Modulus = √(0² + 4²) = √(0 + 16) = √16 = 4.
So, to summarize, the complex conjugate of the number 4i is -4i, and the modulus is 4.