Use the formula to find the missing quantity for the given conditions.The formula E=IZ where E represents voltage,I represents current,and Z represents impedance (a measure of opposition to a sinusoidal electric current),is used in electrical engineering.The variable is a complex number. $$\begin{array} { l }
I = 13 + 5 i \
Z = 4 + 3 i
\end{array}$$
A) $37 + 59 i$
B) $37 - 37 i$
C) $59 - 37 i$
D) $37 - 59 i$
E) $59 + 37 i$

Question

Use the formula to find the missing quantity for the given conditions.The formula E=IZ where E represents voltage,I represents current,and Z represents impedance (a measure of opposition to a sinusoidal electric current),is used in electrical engineering.The variable is a complex number.​ $$\begin{array} { l } 
I = 13 + 5 i \
Z = 4 + 3 i
\end{array}$$ ​
A) $37 + 59 i$
B)​ $37 - 37 i$
C)​ $59 - 37 i$
D)​ $37 - 59 i$
E)​ $59 + 37 i$

Quizplus · Accepted Answer

To find the missing quantity $E = IZ$, we multiply the complex numbers $I = 13 + 5i$ and $Z = 4 + 3i$. The multiplication is done as follows: $(13 + 5i)(4 + 3i) = 52 + 39i + 20i + 15i^2$. Since $i^2 = -1$, this simplifies to $52 + 59i - 15$, which equals $37 + 59i$.

Use the Formula to Find the Missing Quantity for the Given