If `z` is a complex number and `z=bar(z)`, then prove that `z` is a purely real number.

8. If z = x + iy, then show that zz ̅  + 2(z + z ̅ ) + b = 0, where b ∈ represents a circle.

z=z の共役である場合は z が実数であり、z=- z の共役である場合は z が虚であることを証明します。複素数

If z is a complex number of unit modulus and argument θ, then (1+z/1+z) equals (1) -θ (2) π/7-θ (...

Prove that |Z1+Z2|≤ |Z1|+|Z2| and |Z1+Z2|≥ ||Z1|-|Z2|| for Complex Numbers

𝑧 ̅=𝑧 𝑖𝑓𝑓 𝑧 𝑖𝑠 𝑟𝑒𝑎𝑙

If 2z1​/3z2​ is a purely imaginary number, then find the value of ∣(z1​ −z2​ )/(z 1+z2​ )∣

A complex number z is said to be unimodular if |z|=1 | IIT JEE Mains-2015 | Mathematics

7. If (1 + i) z = (1 – i)z ̅ , then show that z = – iz ̅.

Let z and ω be complex numbers such that z ̅+ⅈω ̅=0 and arg(zω)=π then arg(z)= #IIT JEE PROBLEM

If z_1 and z_2 be any two complex numbers such that |z_1+z_2 |=|z_1 |+|z_2 |, then arg〖 z〗_1-arg

If Z is a complex number the radius of z bar z - ( 2+3i)z - (2-3i)barz + 9 =0 is equal to | 12 ...

If| z1| = |z2| = ... = |zn | = 1 , then show that |z1+z2+z3+.....zn| = |1/z1 + 1/z2 + 1/z3+...+1/zn|

if z=x+iy then show that 'z bar(z)+2(z+bar(z))+b=0 'where b in r represents a circle'

If z1 and z2 are two complex numbers such that z2/z1 is a purely imaginary number, then |2z1+3z2| =

9. If the real part of  (z ̅+2)/(z ̅−1)  is 4, then show that the locus of the point representing

|𝑎𝑧+𝑏|=|𝑏 ̅𝑧+𝑎 ̅ | then find |z|

If `|z|+2=I(z)`, then `z=(x,y)` lies on

Complex Equation | Finding Z Modulus

Show that z is real iff 𝑧=conjugate(𝑧).