Section Formula Using Complex Numbers
Trending Questions
Q. In △ABC, A(z1), B(z2) and C(z3) are inscribed in the circle |z|=5. If H(zH) be the orthocentre of △ABC, then zH=
- z1+z2+z33
- z1+z2+z3
- z1+2z2+3z33
- z1+z2+z32
Q. A(z1), B(z2) and C(z3) are the vertices of an isosceles triangle in anticlockwise direction with origin as in-centre. If AB=AC, then z2, z1 and kz3 will form (where k=|z1|2|z2||z3|)
- None of these
- G.P.
- A.G.P.
- A.P.
Q. In △ABC, A(z1), B(z2) and C(z3) are inscribed in the circle |z|=5. If H(zH) be the orthocentre of △ABC, then zH=
- z1+z2+z33
- z1+z2+z3
- z1+z2+z32
- z1+2z2+3z33
Q. If z1, z2, z3 be three non-zero complex number, such that z2≠z1, a=|z1|, b=|z2| and c=|z3| suppose that ∣∣
∣∣abcbcacab∣∣
∣∣=0, then arg (z3z2) is equal to
- arg(z3−z1z2−z1)
- arg(z2−z1z3−z1)2
- arg(z2−z1z3−z1)
- arg(z3−z1z2−z1)2
Q. Let z1, z2, z3 be three complex numbers and a, b, c be real numbers not all zero, such that a+b+c=0 and az1+bz2+cz3=0, then
- z1, z2, z3 are collinear.
- None of these.
- z1, z2, z3 lies on circumference of a circle
- z1, z2, z3 are vertices of a triangle.
Q. If three complex numbers are in A.P .Then they lie on a circle in the complex plane.
- FALSE
- TRUE
Q. Find all complex numbers z which satisfy the following equation:
z=¯z
- x=0
- y=0
- z=0
- x=0, y=0
Q.
The midpoint between and is .
Find .
Q. In △ABC, A(z1), B(z2) and C(z3) are inscribed in the circle |z|=5. If H(zH) be the orthocentre of △ABC, then zH=
- z1+z2+z33
- z1+z2+z3
- z1+z2+z32
- z1+2z2+3z33
Q. Let z1 and z2 be two distinct complex numbers and let z=(1−t)z1+tz2 for some real number t with 0<t<1. If arg(ω) denotes the principal argument of a non-zero complex number ω, then
- |z−z1|+|z+z2|=|z1−z2|
- arg(z−z1) = arg(z−z2)
- ∣∣∣z−z1¯¯¯z−¯¯¯¯¯z1z2−z1¯¯¯¯¯z2−¯¯¯¯¯z1∣∣∣=0
- arg(z−z1) = arg(z2−z1)
Q. x(y+z−x)logx=y(z+x−y)logy=z(z+x−y)logz, then prove that xyyx=zyyz=xzzx.
Q. Let z1 and z2 be two distinct complex numbers and let z=(1−t)z1+tz2 for some real number t with 0<t<1. If arg(ω) denotes the principal argument of a non-zero complex number ω, then
- |z−z1|+|z+z2|=|z1−z2|
- arg(z−z1) = arg(z−z2)
- ∣∣∣z−z1¯¯¯z−¯¯¯¯¯z1z2−z1¯¯¯¯¯z2−¯¯¯¯¯z1∣∣∣=0
- arg(z−z1) = arg(z2−z1)
Q.
Let z1, z2 and z3 be three complex numbers and a, b, c∈R such that a+b+c=0 and az1+bz2+cz3=0 then show that z1, z2 and z3 are collinear.
Q.
If three complex numbers are in A.P., then they lie on
A straight line in the complex plane
A circle in the complex plane
A parabola in the complex plane
None of these
Q. Let z1 and z2 be two non-zero complex numbers such that |z1|+|z2|=|z1+z2|. STATEMENT-1 : amp (z1) = amp (z2)
and
STATEMENT-2 : In complex plane z1, z2 and the origin must be collinear.
and
STATEMENT-2 : In complex plane z1, z2 and the origin must be collinear.
- Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1
- Statement-1 is False, Statement-2 is True
- Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1
- Statement-1 is True, Statement-2 is False
Q. Let z1 and z2 be two distinct complex numbers and let z=(1−t)z1+tz2 for some real number t with 0<t<1. If arg(ω) denotes the principal argument of a non-zero complex number ω, then
- |z−z1|+|z+z2|=|z1−z2|
- arg(z−z1) = arg(z−z2)
- ∣∣∣z−z1¯¯¯z−¯¯¯¯¯z1z2−z1¯¯¯¯¯z2−¯¯¯¯¯z1∣∣∣=0
- arg(z−z1) = arg(z2−z1)
Q. The value of xx−m+yy−n+zz−r is
- 1
- −1
- 2
- −2
Q. If three complex numbers are in A.P., then they lie on
- A circle in the complex plane
- A straight line in the complex plane
- A parabola in the complex plane
- None of these
Q. Which of the following statements is true?
(i) −50 is a negative rational number.
(ii) The reciprocal of 1a, if a=0 is 10.
(iii) 1÷(−14)=−4
(iv) x÷(y+z)=x÷y+x÷z
(i) −50 is a negative rational number.
(ii) The reciprocal of 1a, if a=0 is 10.
(iii) 1÷(−14)=−4
(iv) x÷(y+z)=x÷y+x÷z
- Both (i) and (ii)
- (ii), (iii) and (iv)
- Only (iii)
- (i), (ii) and (iv)
Q. Let x+y∝z+1z, x−y∝z−1z and z=2, when y=1, x=3. Then
- x=215(11z+1z)
- x=2215z−215.1z
- y=215z−2215.1z
- y=215(z+11z)
