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Complex numbers 1 Complex numbers are a crucial tool in the design of modern electrical components, such as motherboards. Electrical engineers use them to simplify many of their calculations. This helps them to analyse varying currents and voltages in electrical circuits. When the current flows in one direction constantly, the resistance can often be calculated using a simple formula. However, when the direction of the current is alternating, this formula doesn’t work. Therefore, engineers express the quantities as complex numbers, which makes it easier to understand the processes involved and perform the necessary calculations. Complex numbers are used in many other fields such as chemistry, economics, and statistics. Their unique properties provide powerful ways of solving and interpreting complicated equations that can be applied in a wide variety of contexts. From some of the deepest mysteries in number theory to the signal processing used in playing digital music, these so-called imaginary numbers have led to a surprising array of advances in the real world. ~\ What you need to know What you will learn What this leads to Ls >| ° To calculate with complex Ch16 Complex numbers 2 © Use the quadratic formula. numbers in the form © Exponential form. a+ ol © The Euler formula Maths Cht To understand and use > oP = 0050+ ising © Solve simultaneous the complex conjugate. © De Moivre's formula. equations. To solve quadratic, cubic © Roots of unity. and quartic equations Maths Ch3 with real coefficients. © Work with sine and cosine | fp] * To convert between pp | cones functions. moculus-argument form ‘ . and the form a+ biand WERE calculate with numbers in moculus-argument form. To sketch and interpret Argand diagrams. » | a A a 
