Question

If $a+ib$ is a root of the equation $x^2-ax+b$, then (where $i=\sqrt{-1}$)

• A. $b=1$
• B. $b=-1$
• C. $b=\pm 1$
• D. none of these

Answer 1

The correct option is A $b=1$

$a+\iota b$ is one root then $a-\iota b$ is another root

$a=a+\iota b+a-\iota b$

$2a=a\Rightarrow a=0$

$(a+\iota b)(a-\iota b)=b$

$a^2+b^2=b$

$b=0,1$