Write the number ` z=(i-sqrt(3))^13` in algebraic form.

Represent the complex numbers z= 1 + sqrt3i into polar form

Let z_(1)= cos 12^(@) + I sin 12^(@) and z_(2) = cos 48^(@) + i. sin 48^(@) . Write complex number (z_(1) + z_(2)) in polar form. Find its modulus and argument.

Express the comple number ((1+sqrt(3)i)^(2))/(sqrt(3)-i) in the form of a+ib . Hence find the modulus and argument of the complex number.

Given the complex number z= (-1 + sqrt3i)/(2) and w= (-1- sqrt3i)/(2) (where i= sqrt-1 ) Calculate the modulus and argument of (w)/(z)

Given the complex number z= (-1 + sqrt3i)/(2) and w= (-1- sqrt3i)/(2) (where i= sqrt-1 ) Represent z and w accurately on the complex plane.

Given the complex number z= (-1 + sqrt3i)/(2) and w= (-1- sqrt3i)/(2) (where i= sqrt-1 ) Calculate the modulus and argument of w and z

Given the complex number z= (-1 + sqrt3i)/(2) and w= (-1- sqrt3i)/(2) (where i= sqrt-1 ) Prove that each of these complex numbers is the square of the other

Write all the terms of each of the following algebraic expressions: (i) 3x (ii) 2x-3

Convert the complex number z=(i-1)/(cospi/3+isinpi/3) in the polar form.

Convert the complex number z=(i-1)/(cospi/3+isinpi/3) in the polar form.