Given
[tex]\begin{gathered} Z_T=\frac{Z_1Z_2}{Z_1+Z_2} \\ Z_1=70+40i,Z_2=50-35i_{} \end{gathered}[/tex]
First, obtain Z_1*Z_2 as shown below
[tex]\begin{gathered} Z_1Z_2=\mleft(70+40i\mright)\mleft(50-35i\mright)=3500+2000i-2450i+1400 \\ \Rightarrow Z_1Z_2=4900-450i=50(98-9i) \end{gathered}[/tex]
On the other hand,
[tex]Z_1+Z_2=(70+40i)+(50-35i)=120+5i=5(24+i)[/tex]
Thus,
[tex]\Rightarrow Z_T=\frac{50(98-9i)}{5(24+i)}=\frac{10(98-9i)}{(24+i)}[/tex]
Finally, the division between complex numbers is given by the formula below
[tex]\frac{a+ib}{c+id}=\frac{(ac+bd)+(bc-ad)i}{c^2+d^2}[/tex]
Therefore, in our case,
[tex]\begin{gathered} \Rightarrow Z_T=10\frac{(98\cdot24-9\cdot1)+(-9\cdot24-98\cdot1)i}{24^2+1^2} \\ \Rightarrow Z_T=10\frac{(2343-314i)}{577} \\ _{} \end{gathered}[/tex]
Rounding to three decimal places,
[tex]\Rightarrow Z_T=40.607-5.442i[/tex]
Thus, the answer is the second option (top to bottom)
