Home
Class 11
MATHS
For any three complex numbers Z(1), Z(2)...

For any three complex numbers `Z_(1), Z_(2), Z_(3)` if `Delta = |(1,Z_(1),bar(Z)_(1)),(1,Z_(2),bar(Z)_(2)),(1,Z_(3),bar(Z)_(3))|`,

A

the real part of `Delta` is always positive

B

the real part of `Delta` is always negative

C

the real part of `Delta` is always zero

D

the imaginary part of `Delta` is always non-zero

Text Solution

Verified by Experts

The correct Answer is:
C
Promotional Banner

Similar Questions

Explore conceptually related problems

For two unimodular complex numbers Z_(1) and Z_(2), [(bar(z_(1)),-z_(2)),(bar(z_(2)),z_(1))]^(-1)[(z_(1),z_(2)),(-bar(z_(2)),bar(z_(1)))]^(-1) is equal to a) [(z_(1),z_(2)),(bar(z)_(1),bar(z)_(2))] b) [(1,0),(0,1)] c) [(1//2,0),(0,1//2)] d)None of these

If z_(1), z_(2), z_(3) are three complex numbers and A= |("arg"z_(1),"arg"z_(2),"arg"z_(3)),("arg"z_(2),"arg"z_(3),"arg"z_(1)),("arg"z_(3),"arg"z_(1),"arg"z_(2))| then A is divisible by

For any two complex numbers z_1 and z_2 prove that Re(z_1z_2) = Re(z_1)Re(z_2) - Im(z_1)Im(z_2)

Consider the complex number z_1 = 3+i and z_2 = 1+i .Find 1/z_2

Consider the complex number z=(1+3i)/(1-2i) .Write z in polar form.

There are three elements A, B, C. Their atomic number are Z_(1),Z_(2)andZ_(3) respectively. If Z_(1)-Z_(2)=2and(Z_(1)+Z_(2))/2=Z_(3)-2 and the electronic configuration of element A is [Ar]3d^(6)4s^(2) then the correct order of magnetic moment of

If the conjugate of a complex number z is (1)/(i-1) , then z is

Consider the complex number z=(1+3i)/(1-2i) . Write z in the form a+ib

If z_(1) and z_(2) are non -zero complex numbers, then show that (z_(1) z_(2))^(-1)=z_(1)^(-1) z_(2)^(-1)

If (z)_(1)=2-i , (z)_(2)=1+i , find |((z)_(1)+(z)_(2)+1)/((z)_(1)-(z)_(2)+1)|