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

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 z is real iff z=conjugate of z and z is imaginary iff z=- conjugate of z | Complex Number

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

𝑧 ̅=𝑧 𝑖𝑓𝑓 𝑧 𝑖𝑠 𝑟𝑒𝑎𝑙

|𝑎𝑧+𝑏|=|𝑏 ̅𝑧+𝑎 ̅ | then find |z|

"If z is a complex number of unit modulus and argument q, then `a r g((1+z)/(1+ bar z))` equal

Let \( z \) be any non-zero complex number. Then \( \arg (z)+\arg (\bar{z}) \) is equal to (A) \...

Calculus Help: Complex Number: z and z bar - Find the solution of z: (1+i)z+z ̅=7+3i

if z argument be the conjugate of a complex number z , prove that arg(z)=2π-arg(z) ||

If z is a complex number which simultaneously satisfies the equations 3|z-12|=5|z-8 i| and |z-4|=...

Find z such that |z|=2 and Arg z = Π/4 | trignometry | Complex Numbers | Complex no | Polar Form

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

Complex Analysis HW (1.2) #3 Algebra of Complex Numbers

Class: 12 Easy way / Properties of Complex Numbers: arg(Z₁/Z₂) = argZ₁ - argZ₂

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

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

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