Question

Given that $A=$ $50+12i$ amps, $B=40-9i$ amps and $C=60-2i$ amps

If the final current is $D=(A+B)\times C$, then $D$ is:

(Note: $i=\sqrt{-1}$)

• A. $5,406$
• B. $3,280$
• C. $4,299$
• D. $5,400$

Answer 1

The correct option is A $5,406$

Given that,

$A=50+12i$, $B=40-9i$ and $C=60-2i$.

Also, $D=(A+B)\times C$.

Put the value of $A,B$ and $C$, we get,

$D=\left[\right(50+12i)+(40-9i)]\times (60-2i)$

$\Rightarrow D=(90+3i)(60-2i)$

$\Rightarrow D=5400+180i-180i-6(i{)}^2$

$\Rightarrow D=5400-6(i{)}^2$.

Put the value given $i=\sqrt{-1}$

$D=5400-6(\sqrt{-1}{)}^2$

$\Rightarrow D=5400-6(-1)$

$\Rightarrow D=5400+6=5406$.