= + z a bi: Consider If = 0, then = We then say that the number is wholly imaginary. a z bi. If = 0, then = We say that the number is real. b z a. If = 0 and = 0, then = 0. a b z Activity 1 For each of the following complex numbers, identify the real and imaginary Real Part [ Imaginary Part [ Complex number a) = 3 + 2i z b) = 3 + 2i z – c) 5 z = i – d) 5 z = – –2i e) 3 z = f) z = –7i g) 0 z = Express each of the following numbers in the form: = + z a bi a) = 3 + 2 b) = + 6 z z –3 c) = 4 + d) = 2 + z z – – e) f) z = z = + – The complex conjugate = + z a bi = a bi If is a complex number, then is called the (or just – complex conjugate the conjugate). Consider the following example: = 5 + 8i and = 5 8i . In this case the real parts are z1 z2 – the same but the imaginary parts have opposite signs, so is the conjugate of z2 z1. Activity 2 Complete the following table Complex Number Conjugate a) = 4 + 5i b) 6 2i = + c) 5 3i = – d) = i – e) 5 = f) = a + bi
Consider z = a + bi: If a = 0, then z = bi. We then say that the number is wholly imaginary. If b = 0, then z = a. We say that the number is real. If a = 0 and b = 0, then z = 0. Activity 1 For each of the following complex numbers, identify the real and imaginary Complex number Real Part [ Imaginary Part [ a) z = 3 + 2i b) z = – 3 + 2i c) z = 5 – i d) z = – 5 –2i e) z = 3 f) z = –7i g) z = 0 Express each of the following numbers in the form: z = a + bi a) z = 3 + 2 b) z = –3 + 6 c) z = – 4 + d) z = – 2 + e) z = – f) z = + The complex conjugate If z = a + bi is a complex number, then = a – bi is called the complex conjugate (or just the conjugate). Consider the following example: z1 = 5 + 8i and z2 = 5 – 8i . In this case the real parts are the same but the imaginary parts have opposite signs, so z2 is the conjugate of z1. Activity 2 Complete the following table Complex Number Conjugate a) = 4 + 5i b) = 6 + 2i c) = 5 – 3i d) = – i e) = 5 f) = a + bi