Solve Q4 explaining detailly each step otherwise, find the roots of the equatiön3. i) Given that the complex numbers z,and z, are the roots of the equation: x² - 4i – 3 = 0.Express z,and z, in the form a + bi where a and b are real.ii) Indicate by shaded areas on separate Argand diagrams the regions defined by:a) /Z + 3/<1_b) /Z+4/>/Z+1/ c) {"< ArgZ < "}n {Im Z < 4}%3D32T- isin -)in the form a + bi, where .:34. a) Given that z = 2- 3i, express i'z, and Z/Z* and Z (cos-44a and b are real.Z+1b) Given thatFi, find z in the forms a + bi, where a and b are real.Z-1c) Given that the complex number 2i represents the point A on the Argand diagram and thatthe point B represents the image of A when reflected in the line y = 2x, find the complexnumber which represents the point B.5. i) Find two complex numbers Z, and Z, which satisfy the simultaneous equationsZ, + Z2 = -i, Z, – iZ2= -4 +iii) Given that Z= 1 + iv3 express Z* in the form|a) a+ bi where a and b are real.b) r(cosq + isinq), where r> 0 and - 1

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4. a) Given that z = 2 – 3i, express i'z, and Z/Z* and Z (cos - isin -) in the form a + bi, where a and b are real. Z+1 b) Given that i, find z in the forms a + bi, where a and b are real. Z-1 c) Given that the complex number 2i represents the point A on the Argand diagram and that the point B represents the image of A when reflected in the line y = 2x, find the complex number which represents the point B.