Q33P - Mathematical Methods in Physical Sciences

Question

Find the absolute value of each of the following using the discussion above. Try to do simple problems like these in your head-it saves time.

 $\frac{\mathbf{25}}{\mathbf{3}\mathbf{+}\mathbf{4}\mathbf{i}}$.

Step-by-Step Solution

Answer

The absolute value is $\left|z\right|=5$ .

Step 1: Given Information

The complex number is $\frac{25}{3+4i}$ .

Step 2: Absolute value of the Complex number

Let z be a complex number consisting of two real numbers as:

  $z=x+ty$

Here x and y are the real numbers.

 

The absolute value of z can be calculated as:

 $\left|\mathrm{z}\right|=\sqrt{{\mathrm{x}}^2+{\mathrm{y}}^2}$

Step 3: Find the value

The complex number is $\frac{25}{3+4i}$ .

 

The absolute value can be calculated as below:

 $$\begin{gathered} \left|z\right|=\left|\frac{25}{3+4i}\right| \\ =\frac{\sqrt{{25}^2}}{\sqrt{9+16}} \\ =\frac{25}{5} \\ \left|z\right|=5 \end{gathered}$$

 

Thus, the final answer is obtained as:$\left|z\right|=5$.