Chapter 1.1, Problem 37E

To determine

To solve the expression $-108\pi =6\pi j$ and verify the solution

Answer to Problem 37E

  $j=-18$

Explanation of Solution

Given:

  $-108\pi =6\pi j$

Calculation:

Now,

  $\Rightarrow -108\pi =6\pi j$

  $\Rightarrow \frac{-108\pi }{6\pi }=\frac{6\pi j}{6\pi }$ (Dividing both sides by $6\pi$ )

  $\Rightarrow j=-18$

Verification:

Now, substitute $j=-18$ in given expression.

  $\begin{array}{l}\Rightarrow -108\pi =6\pi \times \left(-18\right)\\ \Rightarrow -108\pi =-108\pi \end{array}$

Here, Left Hand Side is equal to Right hand side.

So, the obtained solution is correct.

Conclusion:

Hence, the required solution is $j=-18$ .