`bb"Statement-1"` If the principal argument of a complex numbere z is θ ., the principal argument of `z^(2) " is " 2theta`.
`bb"Statement-2" arg(z^(2))=2arg(z)`

If z= sqrt3+i , then the argument of z^2 e^(z-i) is equal to :

If z_(1) and z_(2) are conjugate to each other , find the principal argument of (-z_(1)z_(2)) .

If |z|=2, the points representing the complex numbers -1+5z will lie on

The number of complex numbers z such that |z-1|=|z+1|=|z-i| is

If z is any complex number, prove that : |z|^2= |z^2| .

Let z_(1) and z_(2) be two distinct complex numbers and z=(1-t)z_(1)+tz_(2) , for some real number t with 0 lt t lt 1 and i=sqrt(-1) . If arg(w) denotes the principal argument of a non-zero complex number w, then a. abs(z-z_(1))+abs(z-z_(2))=abs(z_(1)-z_(2)) b. arg(z-z_(1))=arg(z-z_(2)) c. |{:(z-z_(1),bar(z)-bar(z)_(1)),(z_(2)-z_(1),bar(z)_(2)-bar(z)_(1)):}|=0 d. arg(z-z_(1))=arg(z_(2)-z_(1))

If z is purely real number such that Re(z)<0 , then argument (z) is equal to:

If z is a complex number such that |z|geq2 , then the minimum value of |z+1/2|

Find the difference of the complex numbers : z_1=- 3 + 2i and z_2= 13-i .