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

Find the modulus of the complex number z = -3 - i4

Find the modulus of the complex number (2 + 3i)/(2 - 3i)

Find te sum and product of the complex numbers z_1=-sqrt3+sqrt-2 , z_2=2sqrt3-i .

Express in the form of complex number if z=i^(-39)

Express in the form of complex number z= (5-3i)(2+i)

Find the circumstance of the triangle whose vertices are given by the complex numbers z_(1),z_(2) and z_(3) .

A,B and C are the points respectively the complex numbers z_(1),z_(2) and z_(3) respectivley, on the complex plane and the circumcentre of /_\ABC lies at the origin. If the altitude of the triangle through the vertex. A meets the circumcircle again at P, prove that P represents the complex number (-(z_(2)z_(3))/(z_(1))) .

Express in a complex number if z= (2-i)(5+i)

Let A, B, C, D and E be points on the complex plane, which respectively represent the complex numbers z_1,z_2,z_3, z_4 and z_5 . If (z_3 - z_2)z_4 =(z_1- z_2)z_5 , prove that the triangles ABC and DOE are similar.