P3 COMPLEX NUMBERS INSANELY HARD QUESTIONS

Unlock the Mysteries of A-Levels Complex Numbers: Prepare to Be Amazed🤯

Dive into the mind-bending world of A-Levels Complex Numbers as we embark on a thrilling mathematical adventure like no other!
Get ready to:
Unleash the Power of Imaginary Numbers: Watch as we demystify the enigmatic 'i' and explore its mind-boggling properties!
Journey Through the Complex Plane: Take a visual tour through the complex plane and discover its mesmerizing landscapes of real and imaginary axes!
Conquer Complex Equations: Witness the magic of solving complex equations as we unravel their secrets step by step!
Join us for an electrifying journey through the intricate realm of A-Levels Complex Numbers that will not only boost your mathematical prowess but also ignite your passion for the captivating world of numbers! Don't miss out on this epic mathematical adventure!




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Cambridge International AS & A Level Mathematics develops a set of transferable skills. These include the skill of working with mathematical information, as well as the ability to think logically and independently, consider accuracy, model situations mathematically, analyse results and reflect on findings. Learners can apply these skills across a wide range of subjects and the skills equip them well for progression to higher education or directly into employment.




Syllabus Content:
• 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, Imz, modulus of z, arg z, z* should be known.
• 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.
• 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.
• represent complex numbers geometrically by means of an Argand diagram
• carry out operations of multiplication and division of two complex numbers expressed in polar form
Including the results modulus of z1.z2 = modulus z1. modulus z2 and arg a modulus z1.z2 = arg (z1) + arg (z2), and corresponding results for division.
•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.
• understand in simple terms the geometrical effects of conjugating a complex number and of adding, subtracting, multiplying and dividing two complex numbers
• illustrate simple equations and inequalities involving complex numbers by means of loci in an Argand diagram e.g. modulus of z – a is less than k, modulus of z – a = modulus of z – b, arg(z – a) = α.




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0:00 starts
5:29 C2
36:20 Locus concept
52:19 BREAK
1:08:48 C3
2:13:49 BREAK
2:28:31 C4