Question 1 (Learning Outcome No.1) (a) Given the complex numbers Z₁ = 1 + 3i and Z₂ = 2 - i, find (i) Z₁ + Z₂ (ii) Z₁-Z₂

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Question 1 Learning Outcome No 1 A Given The Complex Numbers Z 1 3i And Z 2 I Find I Z Z Ii Z Z 1 (58.26 KiB) Viewed 52 times

Question 1 (Learning Outcome No.1) (a) Given the complex numbers Z₁ = 1 + 3i and Z₂ = 2 - i, find (i) Z₁ + Z₂ (ii) Z₁-Z₂ (iii) |Z₁Z₂| Z₁ (iv) (b) Simplify the following expression: (c) Evaluate (i) (ii) 2i (2+ i)(2- i)(2+31)( 1 (√3+i)³ 1+i√3 √3+i (d) By using De Moivre's theorem, express tan 30 in terms of tan 0. (e) Find all values of Z for which z5 + 32 = 0 for and expressed the roots in polar form. Plot all the roots on an Argand diagram. (4 marks) (3 marks) (4 marks) (7 marks) (7 marks)