1. Evaluate (1+ V3i)' using De Moivre's theorem 2. Evaluate (-1 + j) 3. Express in...

 

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1. Evaluate (1+ V3i)'° using De Moivre's theorem 2. Evaluate (-1 + j) 3. Express in polar form (a) 3+3j, (b) - 2 - 2 3 j 4. Evaluate z + 16 = 0 5. Find all the roots of z* +z +1=0 and locate them in the complex plane. 6. Solve the equation z +(j-2)z+(3- j) =0 7. Find the sixth roots of - 27j 8. Solve z(1-z²) = 16 Hint: z* -z +16= z* +8z +16-9z? = (z' +4+3z)(z² +4-3z) = 0 9. Solve the equation z+1= 3j 10. Find an equation for a circle of radius 4 with center at (-2, 1). 11. A man travels 12 miles northeast, 20 miles 30° west of north, and then 18 miles 60° south of west. Determine (a) analytically and (b) graphically how far and in what direction he is from his starting point. Ans. 14.7Z135.8° %3D 20 30% 12 1. Evaluate (1+ V3i)'° using De Moivre's theorem 2. Evaluate (-1 + j) 3. Express in polar form (a) 3+3j, (b) - 2 - 2 3 j 4. Evaluate z + 16 = 0 5. Find all the roots of z* +z +1=0 and locate them in the complex plane. 6. Solve the equation z +(j-2)z+(3- j) =0 7. Find the sixth roots of - 27j 8. Solve z(1-z²) = 16 Hint: z* -z +16= z* +8z +16-9z? = (z' +4+3z)(z² +4-3z) = 0 9. Solve the equation z+1= 3j 10. Find an equation for a circle of radius 4 with center at (-2, 1). 11. A man travels 12 miles northeast, 20 miles 30° west of north, and then 18 miles 60° south of west. Determine (a) analytically and (b) graphically how far and in what direction he is from his starting point. Ans. 14.7Z135.8° %3D 20 30% 12

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1 Evaluate 13i10 using De Moivres theorem Answer Using De Moivres theorem 13i10 can be written as cos103 isin103 Therefore 13i10 cos103 isin103 12 i32 2 Evaluate 1j Answer Using De Moivres theorem 1j ... View the full answer