International Baccalaureate Mathematics

Syllabus Content

Complex numbers: the number i, where i²=-1. Cartesian form z=a+bi; the terms real part, imaginary part, conjugate, modulus and argument. The complex plane.

Here are some exam-style questions on this statement:

"Consider $ w = a - bi $ where $ |w| = 1 $" ... more

"Consider the complex numbers $z_1 = c + 3i$ and $z_2 = c^2-2-ci$" ... more

See all these questions

Click on a topic below for suggested lesson Starters, resources and activities from Transum.

Number Spotting patterns is an important skill in many areas of life. The world of numbers contains many fascinating patterns and understanding them enables better problem solving strategies. From seeing patterns in the multiples of numbers shaded in a hundred square to spotting the recurring sequences of digits in decimal numbers there is a great deal for pupils to be introduced to. This topic includes even, odd, prime, triangular, perfect, abundant, square and cube numbers. It uses factors and multiples to find solutions to real life problems and encourages number connections to be investigated for pleasure. There are a lot of puzzles, challenges and games too. See also the Mental Methods topic and our Number Skills Inventory.

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Official Guidance, clarification and syllabus links:

The complex plane is also known as the Argand diagram.

Formula Booklet:

Complex numbers

$z=a+bi $

Geometric Sequence:

$$i, i^2, i^3, i^4, i^6, i^7 ... $$ $$=i, -1, -i, 1, i, -1 ... $$

Key Properties:
$$(z^)^=z$$ $$(z_1+z_2)^=z_1^ + z_2^$$ $$(z_1-z_2)^=z_1^* - z_2^$$ $$(z_1z_2)^=z_1^* \times z_2^$$ $$ \left( \dfrac{z_1}{z_2} \right)^ = \dfrac{z_1^}{z_2^}, \quad z_2 \neq 0 $$ $$ (z^n)^* = (z^)^n \text{ for positive integers } n$$ $$z + z^ \text{ and } zz^* \text{ are real}$$ $$|z^|=|z|$$ $$|z|^2 = zz^$$ $$|z_1z_2|=|z_1||z_2|$$ $$\left| \dfrac{z_1}{z_2} \right| = \dfrac{|z_1|}{|z_2|}$$

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International Baccalaureate Mathematics

Number and Algebra

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