New chat PYQ Library Doubts Rank report

Sign in to see Recents

Sign in to save progress →

Complex Numbers question

2022 · 26 Jun · Shift 2 · Q41

Guest · try one question or challengeGuest · try one question or challenge

PYQ Library
JEE Main
Mathematics
Complex Numbers
2022 · 26 Jun · Shift 2 · Q41

Complex Numbers question

2022 · 26 Jun · Shift 2 · Q41

JEE MainMathematicsComplex NumbersNumerical+4 / −1

If

{z^2} + z + 1 = 0

,

z \in C

, then

\left| {\sum\limits_{n = 1}^{15} {{{\left( {{z^n} + {{( - 1)}^n}{1 \over {{z^n}}}} \right)}^2}} } \right|

is equal to

\underline{\hspace{2cm}}

.

Numerical answer

More from Complex Numbers

Let the minimum value $v_{0}$ of $v = ∣ z ∣^{2} + ∣ z - 3 ∣^{2} + ∣ z - 6 i ∣^{2}, z \in C$ is attained at $z = z_{0}$ . Then $2 z_{0}^{2} - \overset{z}{ˉ}_{0}^{3} + 3^{2} + v_{0}^{2}$ is equal to :2022 · MCQ
Let $S = {z \in C : z^{2} + \overset{z}{ˉ} = 0}$ . Then $z \in S \sum (Re (z) + Im (z))$ is equal to .2022 · Numerical
Let S be the set of all $(α, β), π < α, β < 2 π$ , for which the complex number $\frac{1 - i s i n α}{1 + 2 i s i n α}$ is purely imaginary and $\frac{1 + i c o s β}{1 - 2 i c o s β}$ is purely real. Let $Z_{α β} = sin 2 α + i cos 2 β, (α, β) \in S$ …2022 · MCQ
The area of the polygon, whose vertices are the non-real roots of the equation $\overline{z} = i z^{2}$ is :2022 · MCQ
The number of points of intersection of $∣ z - (4 + 3 i) ∣ = 2$ and $∣ z ∣ + ∣ z - 4∣ = 6$ , z $\in$ C, is :2022 · MCQ
Let $S_{1} = {z_{1} \in C : ∣ z_{1} - 3 ∣ = \frac{1}{2}}$ and $S_{2} = {z_{2} \in C : ∣ z_{2} - ∣ z_{2} + 1∣∣ = ∣ z_{2} + ∣ z_{2} - 1∣∣}$ . Then, for $z_{1} \in S_{1}$ and $z_{2} \in S_{2}$ …2022 · MCQ
Let $z = a + ib, b e q 0$ be complex numbers satisfying $z^{2} = \overset{z}{ˉ} \cdot 2^{1 - z}$ . Then the least value of $n \in N$ , such that $z^{n} = (z + 1)^{n}$ , is equal to .2022 · Numerical
The number of elements in the set {z = a + ib $\in$ C : a, b $\in$ Z and 1 < | z $-$ 3 + 2i | < 4} is .2022 · Numerical