If the complex number x = 3 + bi and |x|2 = 13, which is a possible value of b?
We can make use of the modular properties of the complex number.
Answer: The value of b is calculated to be sqrt(133/4).
Go through the steps to understand better.
Given: x = 3 + bi, |x|2 = 13
⇒ |x| = 13/2
Using the definition of modular of a complex number, we get:
|x| = sqrt(32 + b2)
|x| = sqrt(9 + b2)
13/2 = sqrt(9 + b2)
On squaring, on both the sides.
⇒ 169/4 = 9 + b2
⇒ b = sqrt(133/4)