1 Complex Numbers Learning Outcomes 2 Investigate Arithmetic

1 Complex Numbers – Learning Outcomes

2 Investigate Arithmetic

pg 1 3

pg 1 4

pg 2 -3 5

pg 2 -3 6

pg 3 -4 7 Investigate Arithmetic – Add / Subtract

pg 3 -4 8 Investigate Arithmetic – Add / Subtract

pg 3 -4 9 Investigate Arithmetic – Multiply Real

pg 3 -4 10 Investigate Arithmetic – Multiply Real

pg 4 -5 11 Investigate Arithmetic – Multiply Imaginary

pg 4 -5 12 Investigate Arithmetic – Multiply Imaginary

pg 4 -5 13 Investigate Arithmetic – Multiply Imaginary

pg 4 -5 14 Investigate Arithmetic – Multiply Imaginary 2004 OL P 1 Q 4 2007 OL P 1 Q 4 2010 OL P 1 Q 4

pg 4 -5 15 Investigate Arithmetic – Multiply Imaginary 2003 OL P 1 Q 4 2006 OL P 1 Q 4 2011 OL P 1 Q 4

pg 5 -6 16 Calculate the Complex Conjugate

pg 5 -6 17 Calculate the Complex Conjugate e. g. Find the complex conjugate of the following:

pg 5 -6 18 Calculate the Complex Conjugate 2005 OL P 1 Q 4 2011 OL P 1 Q 4

pg 12 -17 19 Solve Quadratics with Complex Roots

pg 12 -17 20 Solve Quadratics with Complex Roots

pg 12 -17 21 Solve Quadratics with Complex Roots

pg 12 -17 22 Solve Quadratics with Complex Roots

pg 12 -17 23 Solve Quadratics with Complex Roots Prove that the following shapes do not intersect:

pg 12 -17 24 Solve Quadratics with Complex Roots 2004 OL P 1 Q 4 2006 OL P 1 Q 4 2009 OL P 1 Q 4

pg 7 -8 25 SP about Fractions of Complex Numbers

pg 7 -8 26 SP about Fractions of Complex Numbers

pg 7 -8 27 SP about Fractions of Complex Numbers Multiply top and bottom by the conjugate of the denominator:

pg 7 -8 28 SP about Fractions of Complex Numbers Distribute the brackets.

pg 7 -8 29 SP about Fractions of Complex Numbers

pg 7 -8 30 SP about Fractions of Complex Numbers

pg 7 -8 31 2013 OL P 1 Q 1 2014 OL P 1 Q 2 SP about Fractions of Complex Numbers

pg 7 -8 32 2006 OL P 1 Q 4 Remember identically equal polynomials! 2003 OL P 1 Q 4 SP about Fractions of Complex Numbers

pg 17 -19 33

pg 17 -19 34

pg 17 -19 35 2005 OL P 1 Q 4 2008 OL P 1 Q 4

pg 17 -19 36 2011(S) OL P 1 Q 3 2011 OL P 1 Q 5

pg 19 -23 37 Solve Problems about Modulus

pg 19 -23 38 Solve Problems about Modulus

pg 19 -23 39 Solve Problems about Modulus 2003 OL P 1 Q 4 2005 OL P 1 Q 4 2006 OL P 1 Q 4

pg 19 -23 40 Solve Problems about Modulus 2012 OL P 1 Q 3

pg 24 -28 41 Discuss and Illustrate Symmetries Recall axial symmetries and rotations from transformation geometry.

pg 24 -28 42 Discuss and Illustrate Symmetries

pg 24 -28 43 Discuss and Illustrate Symmetries

pg 24 -28 44 Discuss and Illustrate Symmetries