:|z| \leq 5\>, S_2=\left\: \operatorname\left(\frac i> i>\right) \geq 0\right.
JEE Main 2024 (Online) 5th April Morning Shift
Consider the following two statements : Statement I: For any two non-zero complex numbers $$z_1, z_2,(|z_1|+|z_2|)\left|\frac<\left|z_1\right|>+\.
JEE Main 2024 (Online) 4th April Evening Shift
The area (in sq. units) of the region $$S=\:|z-1| \leq 2 ;(z+\bar)+i(z-\bar) \leq 2, \operatorname(z) \geq 0\>$$ is
JEE Main 2024 (Online) 4th April Morning Shift
Let $$\alpha$$ and $$\beta$$ be the sum and the product of all the non-zero solutions of the equation $$(\bar)^2+|z|=0, z \in C$$. Then $$4(\alpha^.
JEE Main 2024 (Online) 1st February Evening Shift
If $z$ is a complex number such that $|z| \leqslant 1$, then the minimum value of $\left|z+\frac<1>(3+4 i)\right|$ is :
JEE Main 2024 (Online) 1st February Morning Shift
Let $\mathrm=|\mathrm \in \mathrm:| z-1 \mid=1$ and $(\sqrt-1)(z+\bar)-i(z-\bar)=2 \sqrt \mid$. Let $z_1, z_2 \in \mathrm$ be .
JEE Main 2024 (Online) 31st January Evening Shift
Let $$z_1$$ and $$z_2$$ be two complex numbers such that $$z_1+z_2=5$$ and $$z_1^3+z_2^3=20+15 i$$ Then, $$\left|z_1^4+z_2^4\right|$$ equals -
JEE Main 2024 (Online) 30th January Evening Shift
If $$z$$ is a complex number, then the number of common roots of the equations $$z^<1985>+z^+1=0$$ and $$z^3+2 z^2+2 z+1=0$$, is equal to
JEE Main 2024 (Online) 30th January Morning Shift
If $$z=x+i y, x y \neq 0$$, satisfies the equation $$z^2+i \bar=0$$, then $$\left|z^2\right|$$ is equal to :
JEE Main 2024 (Online) 29th January Evening Shift
Let $$\mathrm$$ and $$\theta$$ respectively be the modulus and amplitude of the complex number $$z=2-i\left(2 \tan \frac\right)$$, then $.
JEE Main 2024 (Online) 29th January Morning Shift
If $$z=\frac<1>-2 i$$ is such that $$|z+1|=\alpha z+\beta(1+i), i=\sqrt$$ and $$\alpha, \beta \in \mathbb$$, then $$\alpha+\beta$$ is equal .
JEE Main 2024 (Online) 27th January Morning Shift
If $S=\$, then, $n(S)$ is :
JEE Main 2023 (Online) 15th April Morning Shift
If the set $\left\<\operatorname\left(\frac+z \bar><2-3 z+5 \bar>\right): z \in \mathbb, \operatorname(z)=3\right\>$ is equ.
JEE Main 2023 (Online) 13th April Evening Shift
JEE Main 2023 (Online) 12th April Morning Shift
Let $$\mathrm$$ be the circle in the complex plane with centre $$\mathrm_=\frac(1+3 i)$$ and radius $$r=1$$. Let $$\mathrm_=1+\ma.
JEE Main 2023 (Online) 11th April Evening Shift
JEE Main 2023 (Online) 11th April Morning Shift
Let $$w_<1>$$ be the point obtained by the rotation of $$z_<1>=5+4 i$$ about the origin through a right angle in the anticlockwise direction, and $$w_.
JEE Main 2023 (Online) 10th April Evening Shift
Let $$S = \left\ < \over >\,\mathrm> \right\>$$. Then which of the following is NOT correct.
JEE Main 2023 (Online) 10th April Morning Shift
Let the complex number $$z = x + iy$$ be such that $$ <<2z - 3i>\over >$$ is purely imaginary. If $$ + = 0$$, then $$ + - .
JEE Main 2023 (Online) 8th April Evening Shift
Let $$A=\left\\right.$$ is purely imaginary $$\>$$. Then the sum of the elements in $$.
JEE Main 2023 (Online) 8th April Morning Shift
If for $$z=\alpha+i \beta,|z+2|=z+4(1+i)$$, then $$\alpha+\beta$$ and $$\alpha \beta$$ are the roots of the equation :
JEE Main 2023 (Online) 6th April Evening Shift
Let $$a \neq b$$ be two non-zero real numbers. Then the number of elements in the set $$X=\left\: \operatorname\left(a z^+b z\.
JEE Main 2023 (Online) 1st February Evening Shift
Let $$a,b$$ be two real numbers such that $$ab .
JEE Main 2023 (Online) 1st February Morning Shift
If the center and radius of the circle $$\left| <<\over >> \right| = 2$$ are respectively $$(\alpha,\beta)$$ and $$\gamma$$, then $$3(\.
JEE Main 2023 (Online) 31st January Evening Shift
The complex number $z=\frac+i \sin \frac<\pi>>$ is equal to :
JEE Main 2023 (Online) 31st January Morning Shift
For all $$z \in C$$ on the curve $$C_<1>:|z|=4$$, let the locus of the point $$z+\frac<1>$$ be the curve $$\mathrm_$$. Then :
JEE Main 2023 (Online) 29th January Morning Shift
For two non-zero complex numbers $$z_<1>$$ and $$z_$$, if $$\operatorname\left(z_ <1>z_\right)=0$$ and $$\operatorname\left(z_<1>+z_\.
JEE Main 2023 (Online) 25th January Evening Shift
Let $$z$$ be a complex number such that $$\left| <<\over >> \right| = 2,z \ne - i$$. Then $$z$$ lies on the circle of radius 2 and ce.
JEE Main 2023 (Online) 25th January Morning Shift
Let $$\mathrm$$ and $$\mathrm$$. The set $$\mathrm:<<\left| > \right|>^2> - <<\left|
JEE Main 2023 (Online) 24th January Evening Shift
The value of $$ <\left( <<\over 9> + i\cos <<2\pi >\over 9>> \over \over 9> - i\cos <<2\pi >\over 9>>>> \right).
JEE Main 2023 (Online) 24th January Morning Shift
Let $$\mathrm>$$ and $$ <\left( <1 - \sqrt 3 i>\right)^> = >(p + iq),i = \sqrt < - 1>$$ then $$\mathrm$$ and $.
JEE Main 2022 (Online) 29th July Evening Shift
If $$z \neq 0$$ be a complex number such that $$\left|z-\frac<1>\right|=2$$, then the maximum value of $$|z|$$ is :
JEE Main 2022 (Online) 29th July Evening Shift
Let $$\mathrm=\
JEE Main 2022 (Online) 29th July Morning Shift
If $$z=2+3 i$$, then $$z^<5>+(\bar)^<5>$$ is equal to :
JEE Main 2022 (Online) 28th July Morning Shift
Let $$S_<1>=\left\ \in \mathbf:\left|z_<1>-3\right|=\frac<1>\right\>$$ and $$S_=\left\
JEE Main 2022 (Online) 27th July Evening Shift
Let S be the set of all $$(\alpha, \beta), \pi.
JEE Main 2022 (Online) 27th July Morning Shift
Let the minimum value $$v_<0>$$ of $$v=|z|^+|z-3|^+|z-6 i|^, z \in \mathbb$$ is attained at $$< >=z_<0>$$. Then $$\left|2 z_<0>^-\b.
JEE Main 2022 (Online) 26th July Evening Shift
If $$z=x+i y$$ satisfies $$|z|-2=0$$ and $$|z-i|-|z+5 i|=0$$, then :
JEE Main 2022 (Online) 26th July Morning Shift
Let O be the origin and A be the point $$ = 1 + 2i$$. If B is the point $$$$, $$<\mathop<\rm Re>\nolimits> () .
JEE Main 2022 (Online) 25th July Evening Shift
For $$z \in \mathbb$$ if the minimum value of $$(|z-3 \sqrt|+|z-p \sqrt i|)$$ is $$5 \sqrt$$, then a value Question: of $$p$$ is _________.
JEE Main 2022 (Online) 25th July Morning Shift
For $$\mathrm \in \mathbf$$, let $$\mathrm_<\mathrm>=\left\:|z-3+2 i|=\frac<\mathrm>\right\>$$ and $$\mathrm_<\m.
JEE Main 2022 (Online) 30th June Morning Shift
The real part of the complex number $$<<<<(1 + 2i)>^8>\,.\,<<(1 - 2i)>^2>> \over <(3 + 2i)\,.\,\overline <(4 - 6i)>>>$$ is equal to :
JEE Main 2022 (Online) 29th June Evening Shift
Let arg(z) represent the principal argument of the complex number z. Then, |z| = 3 and arg(z $$-$$ 1) $$-$$ arg(z + 1) = $$<\pi \over 4>$$ intersect .
JEE Main 2022 (Online) 29th June Morning Shift
Let $$\alpha$$ and $$\beta$$ be the roots of the equation x2 + (2i $$-$$ 1) = 0. Then, the value of |$$\alpha$$8 + $$\beta$$8| is equal to .
JEE Main 2022 (Online) 27th June Evening Shift
The number of points of intersection of $$|z - (4 + 3i)| = 2$$ and $$|z| + |z - 4| = 6$$, z $$\in$$ C, is :
JEE Main 2022 (Online) 27th June Morning Shift
The area of the polygon, whose vertices are the non-real roots of the equation $$\overline z = i$$ is :
JEE Main 2022 (Online) 26th June Morning Shift
Let $$A = \left\ < \over >> \right| .
JEE Main 2022 (Online) 25th June Evening Shift
Let z1 and z2 be two complex numbers such that $$ <\overline z _1>= i<\overline z _2>$$ and $$\arg \left( > \over <<<\overline z >_2>>>> \righ.
JEE Main 2022 (Online) 25th June Morning Shift
Let a circle C in complex plane pass through the points $$ = 3 + 4i$$, $$ = 4 + 3i$$ and $$ = 5i$$. If $$z( \ne )$$ is a point on .
JEE Main 2022 (Online) 24th June Morning Shift
Let $$A = \ < z \in C:1 \le |z - (1 + i)| \le 2\>$$ and $$B = \ < z \in A:|z - (1 - i)| = 1\>$$. Then, B :
JEE Main 2021 (Online) 31st August Evening Shift
If z is a complex number such that $$ <\over >$$ is purely imaginary, then the minimum value of | z $$-$$ (3 + 3i) | is :
JEE Main 2021 (Online) 27th August Morning Shift
If $$S = \left\ < \over > \in R> \right\>$$, then :
JEE Main 2021 (Online) 26th August Evening Shift
If $$ <\left( <\sqrt 3 + i>\right)^> = >(p + iq)$$, then p and q are roots of the equation :
JEE Main 2021 (Online) 26th August Morning Shift
The equation $$\arg \left( <<\over >> \right) = <\pi \over 4>$$ represents a circle with :Let C be the set of all complex numbers. LetS1 = and S2 =
JEE Main 2021 (Online) 27th July Morning Shift
Let C be the set of all complex numbers. Let$$ = \ < z \in C||z - 3 - 2i<|^2>= 8\> $$$$ = \< z \in C|<\mathop<\rm Re>\nolimits> (z) \ge 5\> .
JEE Main 2021 (Online) 22th July Evening Shift
Let n denote the number of solutions of the equation z2 + 3$$\overline z $$ = 0, where z is a complex number. Then the value of $$\sum\limits_^.
JEE Main 2021 (Online) 20th July Morning Shift
If z and $$\omega$$ are two complex numbers such that $$\left| \right| = 1$$ and $$\arg (z) - \arg (\omega ) = <<3\pi >\over 2>$$, then $$.
JEE Main 2021 (Online) 18th March Evening Shift
Let a complex number be w = 1 $$-$$ $$$$i. Let another complex number z be such that |zw| = 1 and arg(z) $$-$$ arg(w) = $$<\pi \over 2>$$. .
JEE Main 2021 (Online) 18th March Morning Shift
If the equation $$a|z <|^2>+ \overline <\overline \alpha z + \alpha \overline z >+ d = 0$$ represents a circle where a, d are real constants then w.
JEE Main 2021 (Online) 17th March Evening Shift
Let S1, S2 and S3 be three sets defined asS1 = S2 = S3 = The area of the triangle with vertices A(z), B(iz) and C(z + iz) is :
JEE Main 2021 (Online) 16th March Evening Shift
The least value of |z| where z is complex number which satisfies the inequality $$\exp \left( <<<(|z| + 3)(|z| - 1)>\over <||z| + 1|>><<\log >_e>2> \.
JEE Main 2021 (Online) 16th March Morning Shift
Let a complex number z, |z| $$\ne$$ 1, satisfy $$<\log _<<1 \over <\sqrt 2 >>>>\left( <<<|z| + 11>\over <<<(|z| - 1)>^2>>>> \right) \le 2$$. Then, th.
JEE Main 2021 (Online) 25th February Evening Shift
If $$\alpha$$, $$\beta$$ $$\in$$ R are such that 1 $$-$$ 2i (here i2 = $$-$$1) is a root of z2 + $$\alpha$$z + $$\beta$$ = 0, then ($$\alpha$$ $$-$$ $.
JEE Main 2021 (Online) 25th February Morning Shift
Let the lines (2 $$-$$ i)z = (2 + i)$$\overline z $$ and (2 $$+$$ i)z + (i $$-$$ 2)$$\overline z $$ $$-$$ 4i = 0, (here i2 = $$-$$1) be normal to a ci.
JEE Main 2020 (Online) 6th September Evening Slot
Let z = x + iy be a non-zero complex number such that $$ = i<\left| z \right|^2>$$, where i = $$\sqrt < - 1>$$ , then z lies on the :
