Question

Find $a$ and $b$, where $a$ and $b$ are real numbers so that
$a+ib={(2-i)}^2$

• A. $a=3,b=-4$
• B. $a=-3,b=-4$
• C. $a=3,b=4$
• D. $a=-3,b=4$

Answer 1

The correct option is A $a=3,b=-4$

Solve the given expression as follows:

$a+ib=(2-i{)}^2$

$a+ib=4+i^2-4i$

$a+ib=4-1-4i$

$a+ib=3-4i$

The real term on the left is $a$, the real term on the right is $3$. These two are equal.

The imaginary term on the left is $b$ and the imaginary term on the right is $-4$. These two are equal.

Therefore, $a=3$, and $b=-4$.