Question

lf $i=\sqrt{-1}$, then the number of real roots of $z^3+iz-1=0$ is

• A. $0$
• B. $1$
• C. $2$
• D. $3$

Answer 1

Answer: (A)

$0$

$z^3+iz-1=0$
Let $x$ be a real root of the equation.
Then,

$x^3+ix-1=0$
Since x is real, comparing real and imaginary ports
$\Rightarrow x^3-1=0$ & $x=0$
$\Rightarrow x=1$ & $x=0$
This is not possible. Hence, there are no real roots of the equation.