Chapter 7, Problem 7.1CYU

Check Your Understanding If $a=3+4i$ , what is the product a* a?

To determine

To calculate:

The product of $a*a$, where $a=3+4i$.

Answer to Problem 7.1CYU

The product of $a*a$ where $a=3+4i$ is 25.

Explanation of Solution

Given:

  $a=3+4i$

Formula used:

The complex function is the one which contains one or more imaginary number $(i=\sqrt{-1})$. The complex conjugate of a function is determined by replacing every occurrence of $(i=\sqrt{-1})$ in that function with −i.

Calculation:

a* = complex conjugate of a.

  $\begin{array}{l}a=3+4i\\ \Rightarrow a*=3-4i\end{array}$ of

To determine the magnitude of $\left(a*\right)\left(a\right),$ substitute the values

  $\begin{array}{l}\left(a*\right)\left(a\right)=\left(3-4i\right)\left(3+4i\right)\hfill \\ =9+16\hfill \\ \left(a*\right)\left(a\right)=25.\hfill \end{array}$

Conclusion:

Thus, the product of $\left(a*\right)\left(a\right)=25$.