= 3 ; = 3 x y – Determine the argument of: 1. = 3-3i z = 1 ; = 2 x y – Determine the of: argument 2. = 1 + 2i z – tan = 2 – = 116,57o = arg z = 0,6476 = 1 ; = 1 x y – – = = 1 = . But this angle lies in the third quadrant, so to calculate the arg z( i.e. the angle from Determine the argument of : the positive real axis or in a clockwise 3. = 1 direction) is : arg z = = z i – – – If the angle is measure anti-clockwise, then the angle will be: = = = 2 ; = x y 2 Determine the argument of: 4. = = = 2 + 2 z i = arg z = Activity 8 Determine the argument of the following complex numbers Complex Complex arg z Number (z) Number (z) a) 4 b) 3i c) 3 d) i – – e) 1 + f) 2 2i i – g) 1 + h) i i –1 – i) j) 2 + i i – k) 1–3i l) 1 + 3i – Given: = z Write in the form z a + bi Hence determine the modulus and argument of z
1. Determine the argument of: z = 3-3i x = 3 ; y = – 3 2. Determine the argument of: z = – 1 + 2i x = – 1 ; y = 2 tan = – 2 = 116,57o = arg z = 0,6476 3. Determine the argument of : z = – 1 – i x = – 1 ; y = – 1 = = 1 = . But this angle lies in the third quadrant, so to calculate the arg z( i.e. the angle from the positive real axis or in a clockwise direction) is : arg z = – = If the angle is measure anti-clockwise, then the angle will be: = = 4. Determine the argument of: z = 2 + 2 i x = 2 ; y = 2 = = = arg z = Activity 8 Determine the argument of the following complex numbers Complex Number (z) arg z Complex Number (z) a) 4 b) 3i c) – 3 d) – i e) 1 + i f) 2 – 2i g) 1 + i h) –1 – i i) – i j) 2 + i k) 1–3i l) – 1 + 3i Given: z = Write z in the form a + bi Hence determine the modulus and argument of z
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