What you’ll learn8 learning objectivesChoose one objective for a focused lesson, or study the complete topic.3.9.1Complex numbers• understand the idea of a complex number, recall the meaning of the terms real part, imaginary part, modulus, argument, conjugate, and use the fact that two complex numbers are equal if and only if both real and imaginary parts are equal Notations Re z, Im z, |z|, arg z, z* should be known. The argument of a complex number will usually refer to an angle i such that 1 G-rr i, but in some cases the interval 02 1G ri may be more convenient. Answers may use either interval unless the question specifies otherwise.Syllabus objective3.9.2Complex numbers• carry out operations of addition, subtraction, multiplication and division of two complex numbers expressed in Cartesian form x + iy For calculations involving multiplication or division, full details of the working should be shown.Syllabus objective3.9.3The result that• use the result that, for a polynomial equation with real coefficients, any non-real roots occur in conjugate pairs e.g. in solving a cubic or quartic equation where one complex root is given.Syllabus objective3.9.4Complex numbers• represent complex numbers geometrically by means of an Argand diagramSyllabus objective3.9.5Complex numbers• carry out operations of multiplication and division of two complex numbers expressed in polar form coss inrr i ei/ii+ i^h Including the results |z1z2| = |z1||z2| and arga rg argzz zz12 12= +__ _ii i, and corresponding results for division.Syllabus objective3.9.6Complex numbers• find the two square roots of a complex number e.g. the square roots of 5 + 12i in exact Cartesian form. Full details of the working should be shown.Syllabus objective3.9.7Complex numbers• understand in simple terms the geometrical effects of conjugating a complex number and of adding, subtracting, multiplying and dividing two complex numbersSyllabus objective3.9.8Complex numbers• illustrate simple equations and inequalities involving complex numbers by means of loci in an Argand diagram. e.g. |z - a| < k, |z - a| = |z - b|, arg(z - a) = α.Syllabus objective