Consider the following statements. I. The value of $x^3+7 x^2-x+16$, when $x=1+2 i$ is $-17+24 {i}$. II. If $i z^3+z^2-z+i=0$ then $|z|=1$ Choose the correct option.

JEE MATHEMATICS MCQ: COMPLEX NUMBERS

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Application +4 | -1

Consider the following statements.

I. The value of

x^3+7 x^2-x+16

, when

x=1+2 i

-17+24 {i}

.

II. If

i z^3+z^2-z+i=0

then

|z|=1

Choose the correct option.

View answer and explanation

Correct option: C

Both are correct

Option C (Both are correct) is correct because both statements are true after evaluating the polynomial at x=1+2i and solving the cubic equation.

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{\left| {1 - i} \right|^x} = {2^x}

|z|=1

z \neq \pm 1

z, \frac{z}{1-z^2}

\left|z_r-r\right| \leq r, \forall r=1,2,3, \ldots, n

\left|\sum\limits_{r=1}^n z_r\right|

(z+a b)^3=a^3

a \neq 0

\alpha, \beta

\gamma

|\alpha-\beta|

{z^2} + {\left| z \right|^2} = 0,

z \in C

2x = - 1 + \sqrt 3 i

{\left( {1 - {x^2} + x} \right)^6} - {\left( {1 - x + {x^2}} \right)^6}