Question

(a) Find the two complex square roots of -3 - 4i. Hence, or otherwise, solve the quadratic equation z^2 + (3 + 2i)z + 2 + 4i = 0. (b) Write down the six (complex) sixth roots of unity in Cartesian form. (That is, the solutions of ω^6 = 1). Write -i in polar form. Hence, or otherwise, find the six sixth roots of -i, that is, the solutions of z^6 = -i in polar/exponential form. (c) Write down the three (complex) cube roots of unity in Cartesian form. (That is, the solutions of ω^3 = 1). Write -2 + 2i in polar form. Hence, or otherwise, find the three cube roots of -2 + 2i, that is, the solutions of z^3 = -2 + 2i in Cartesian form.

          (a) Find the two complex square roots of -3 - 4i. Hence, or otherwise, solve the quadratic equation z^2 + (3 + 2i)z + 2 + 4i = 0.
(b) Write down the six (complex) sixth roots of unity in Cartesian form. (That is, the solutions of ω^6 = 1). Write -i in polar form. Hence, or otherwise, find the six sixth roots of -i, that is, the solutions of z^6 = -i in polar/exponential form.
(c) Write down the three (complex) cube roots of unity in Cartesian form. (That is, the solutions of ω^3 = 1). Write -2 + 2i in polar form. Hence, or otherwise, find the three cube roots of -2 + 2i, that is, the solutions of z^3 = -2 + 2i in Cartesian form.

Added by Lisa T.

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