Q26P - 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.

 $\frac{\mathbf{2}\mathbf{i}\mathbf{-}\mathbf{1}}{\mathbf{i}\mathbf{-}\mathbf{2}}$.

Step-by-Step Solution

Answer

The absolute value is $\left|z\right|=1$ .

Step 1: Given Information

The complex number is $\frac{2i-1}{i-2}$.

Step 2: Absolute valueof the Complex number

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

$\mathit{z}\mathbf{=}\mathit{x}\mathbf{+}{}_{\mathbf{z}}\mathit{y}$

Here x and y are the real numbers.

 

The absolute value of z can be calculated as:

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

Step 3: Find the value

The complex number is $\frac{2i-1}{1-2}$ .

 

The absolute value can be calculated as below:

$$\begin{gathered} \left|z\right|=\left|\frac{2i-1}{i-2}\right| \\ \left|z\right|=\left|\frac{2i-1}{i-2}\right| \\ \left|z\right|=\frac{\sqrt{4+1}}{\sqrt{1+4}} \\ \left|z\right|=1 \end{gathered}$$

Thus, the final answer is obtained as:

$\left|z\right|=1$

 .