Question 1
Three complex numbers are given in the table below. For each complex number, find the modulus and the principal argument, giving your argument in radians to 2 decimal places.
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Specialist Mathematics Β· Unit 2 Β· Complex arithmetic and algebra Β· Complex arithmetic using polar form
Use the modulus |π§| of a complex number π§ and the principal argument Arg(π§) of a non-zero complex number π§. |π§| = βπ2 + π2 Arg(π§) = π, tan(π) = π π, βπ < π β€ π, π β 0
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Question 2
Let \(w = 3 - 4i\) and \(z = -2 + 5i\). (a) Determine \(|w|\). (1 mark) (b) Determine \(\text{Arg}(z)\), giving your answer in radians correct to two decimal places. (2 marks) (c) Determine \(\text{Arg}\left(\frac{w}{z}\right)\), giving your answer in radians correct to two decimal places. (1 mark)
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Question 3
What is the principal argument Arg(z) of the complex number z = -1 + β3i?
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