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1. a) Draw a sketch of: {z∈C|Im((3−2i)z)>6}. b) If 2i is a zero of p(z)=az^2+z^3+bz+16, find...

1.
a) Draw a sketch of: {z∈C|Im((3−2i)z)>6}.
b) If 2i is a zero of p(z)=az^2+z^3+bz+16, find the real numbers a,b.
c) Let p(z)=z^4−z^3−2z^2+a+6z, where a is real. Given that 1+i is a zero of p(z):

Find value of a, and a real quadratic factor of p(z). Express p(z)as a product of two real quadratic factors to find all four zeros of p(z).
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