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Complex Numbers

Complex Numbers is an important topic in algebra that extends the concept of real numbers. A complex number is a number that has both a real part and an imaginary part and is usually written in the form a + ib, where a and b are real numbers and i is the imaginary unit. In this topic, students learn how to perform operations with complex numbers and understand their properties. Complex numbers are widely used in mathematics, engineering, physics, and signal processing.

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Important Points
Complex Numbers – Important Points & Formulae (MHT-CET) 1. Definition A complex number is written as z=a+ib. Where π‘Ž a = Real part 𝑅 𝑒 ( 𝑧 ) Re(z) 𝑏 b = Imaginary part 𝐼 π‘š ( 𝑧 ) Im(z) 𝑖 = βˆ’ 1 i= βˆ’1 ​ This PDF contains complete and easy revision notes for Complex Numbers (MHT-CET Maths). It covers all the important concepts, formulas, and properties needed to solve exam questions quickly. Topics included in this PDF: β€’ Definition of complex numbers β€’ Real and imaginary parts β€’ Powers of 𝑖 i β€’ Conjugate of complex numbers β€’ Modulus and argument β€’ Argand plane representation β€’ Polar form of complex numbers β€’ De Moivre’s theorem β€’ Roots of complex numbers β€’ Important identities and formulas These notes are designed for quick revision before MHT-CET 2026 and will help you solve MCQs faster in the exam.

Formula Bank

Modulus of Complex Number
|Z|=\sqrt{a^2+b^2}
Argument of Complex Number
arg(z)=\theta\space where\space\theta=\tan^{\prime}\left(\frac{b}{a}\right)\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space Principal\space argument:-\pi<Arg(z)\le\pi
Polar Form of Complex Number
z=r(cos\theta+isin\theta)\space Where\space\space\space,\spaceπ‘Ÿ=\vert𝑧\vert\space\space\space\space\space\space\space\spaceπœƒ=π‘Žπ‘Ÿπ‘”(𝑧)
Euler Form
𝑧=π‘Ÿe^{i\theta}
Conjugate of Complex Number
If\space\space\space𝑧=π‘Ž+𝑖𝑏\space\space\space\space\space Then\space\space\space conjugate\space is\space\space\space\space𝑧ˉ=π‘Ž-𝑖𝑏\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space
Circular Permutation
(nβˆ’1)!
Combination (Selection)
nCr=\frac{r!}{(n-r)!n!}

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