Question

Solving $3-2yi=9^x-7i$, where $i^2=-1$ for $xandy$ real, we get

• A. $x=0.5,y=3.5$
• B. $x=5,y=3$
• C. $x=\frac{1}{2},y=7$
• D. $x=0,y=\frac{(3+7i)}{2i}$

Answer 1

The correct option is A

$x=0.5,y=3.5$

Step 1: Given Data:

$3-2yi=9^x-7i$

Step 2: In comparing real and imaginary parts,

$9^x=3\mathrm{and}2y=7$

Step 3: Solving for the value of $x$,

$\begin{array}{rcl}{9}^x& =& 3\\ {\left(3^2\right)}^x& =& 3\\ {\left(3\right)}^{2x}& =& 3\\ 2x& =& 1\\ x& =& \frac{1}{2}\\ & =& 0.5\end{array}$

Step 4: Solving for the value of $y$,

$\begin{array}{rcl}2y& =& 7\\ y& =& \frac{7}{2}\\ & =& 3.5\end{array}$

Hence option (a) is correct.