Find real numbers $a$ and $b$ such that the equation $a + b i = 10 - 12 i$ is true.
A) $a = - 10 , b = 12$
B) $\quad a = 10 , b = 12$
C) $\quad a = - 10 , b = - 12$
D) $\quad a = 10 , b = - 12$
E) $\quad a = 22 , b = - 2$

Question

Quizplus · Accepted Answer

To find the values of $a$ and $b$, we can equate the real part of the left-hand side of the given equation with the real part of the right-hand side, and the imaginary part of the left-hand side with the imaginary part of the right-hand side. This gives us:
\begin{align*}
a &= 10 \
bi &= -12i \quad \Rightarrow \quad b = -12
\end{align*}
Therefore, the values of $a$ and $b$ that satisfy the equation are $a = 10$ and $b = -12$, which corresponds to choice D.

Find Real Numbers aaa And bbb Such That the Equation a+bi=10−12ia + b i = 10 - 12 ia+bi=10−12i

Find Real Numbers $a$ And $b$ Such That the Equation $a + b i = 10 - 12 i$