" EXAMPLE 29If "z=2+i" ,prove that "z^(3)+3z^(2)-9z+8=(1+14i)

If z= -3 + sqrt2i , then prove that z^(4) + 5z^(3) + 8z^(2) + 7z + 4 is equal to -29

If z = 3 + 2i , prove that z^(2) - 6z + 13 = 0 and hence deduce that 3z^(3) - 13z^(2) + 9z + 65 = 0 .

If z_(1)=3+4i" and "z_(2)=2-i , verify that |z_(1)z_(2)|=|z_(1)||z_(2)| .

If z_(1)=3 + 4i,z_(2)= 8-15i , verify that |z_(1) + z_(2)| lt |z_(1)| + |z_(2)|

If z_(1)=3 + 4i,z_(2)= 8-15i , verify that |z_(1)z_(2) |= |z_(1)| |z_(2)|

If z_(1)=3 + 4i,z_(2)= 8-15i , verify that |z_(1) + z_(2)|^(2) + |z_(1)-z_(2)|^(2)= 2(|z_(1)|^(2) + |z_(2)|^(2))

If z_(1)=-3i,z_(2)=3+4i and z_(3)=2-3i , verify that z_(1)(z_(2)+z_(3))=z_(1)z_(2)+z_(1)z_(3) .

If z=4+i sqrt(7) then the value of Z^(3)-4Z^(2)-9z+91 equal

If z_(1)=iz_(2) and z_(1)-z_(3)=i(z_(3)-z_(2)), then prove that |z_(3)|=sqrt(2)|z_(1)|

If Z_1 = -3 + 4i , Z_2 = 12 - 5i , prove that |z_1+z_2|<|z_1-z_2|