(i) Solve \(z^2+3iz+2=0\) over the complex number field. (2 marks)
(ii) Solve \({z^2} + (4 + 2i)z + 6 + 8i = 0\) over the complex number field (3 marks)
(i) \(z = \dfrac{{ - 3i \pm i\sqrt {17} }}{2}\)
(ii) \(z = 1 + 3i\) or \(z = 3-i\)
(i) Solve \(4{z^3} - i{z^2} - 4z + i = 0\) over the complex field. (3 marks)
(ii) Solve \({z^2} + 4z + 1 - 4i = 0\) over the complex field. (3 marks)
(i) \(z = \pm 1\) or \(z = \dfrac{1}{4}i\)
(ii) \(z=i\) or \(z=-4-i\)
Given that \( - i{\rm{ }}\) is a zero of \({\rm{ }} P(x) = {x^3} + i{x^2} - 4x - 4i{\rm{ }}\) then the other zeros are?
\(2\) and \( - 2\)
The solutions to \({z^2} - \left( {1 - 4i} \right)z - \left( {5 - i} \right) = 0{\rm{ }}\) are?
\(2 - 3i, - 1 - i\)
Show that if \(i\) is a zero of \(P(z) = {z^3} - i{z^2} + 4z - 4i\) then the other zeros are ?
\( \pm \,2i\)
The solutions to \({z^2} + 2iz + 3 = 0\) are?
\(-3i, i\)
The solutions to \(4{z^2} - 8z + 1 - 4i = 0\) are?
\(\dfrac{{4 + i}}{2}, - \dfrac{i}{2}\)
The solutions to \(2{z^2} + 2z - 3 - 12i = 0\) are?
\(\dfrac{{3 + 3i}}{2},\dfrac{{ - 5 - 3i}}{2}\)
The solutions to \({z^2} - \left( {3 + i} \right)z + 4 + 3i = 0\) are?
\(2 - i,\,\,1 + 2i\)
Solve \(z^2+(1+i)z+i=0\)
\( z=-i \text { or } z=-1\)
