Complex Number



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Contents

Algebra of Complex Numbers


Description: Mathematical branch dealing with operations, properties, and applications of complex numbers, involving real and imaginary components.


Ex. 10.1


Description: Ex. 10.1 Solution


Root & Theorem & Ex.10.2


Description: The square root of a complex number is a number that, when squared, equals the original number. The Fundamental Theorem of Algebra states that every polynomial equation has at least one root.


Ex.10.2 Part -II


Description: Ex.10.2 Part -II Solution


Ex.10.2 Part -III


Description: Ex.10.2 Part -III Solution


Ex 10.3 Part -III


Description: Ex 10.3 Part -III Solution


Ex. 10.1 Part-II


Description: Ex. 10.1 Part-II Solution


Ex.10.2 Part -IV


Description: Ex.10.2 Part -IV Solution


Triginometric Ratios Sign & Changes


Description: Trigonometric ratios' signs change by quadrant: All positive (Q1), sine positive (Q2), tangent positive (Q3), cosine positive (Q4).


Ex.10.3


Description: Ex.10.3 Solution


De Moivres Theorem & Ex. 10.4 Part-III


Description: De Moivre's Theorem relates complex numbers and trigonometry, expressing powers of complex numbers using angles, facilitating computation of roots and powers Ex. 10.4 Part-III Solutions.


Ex.10.4 Part-IV


Description: Ex.10.4 Part-IV Solution


Ex 10.3 Part -II


Description: Ex 10.3 Part -III Solution


Cube roots of unity & Ex.10.4


Description: The cube roots of unity are 1, omega, and omega squared. Properties: cyclic, non-real, multiply to one, sum to zero, and evenly spaced on unit circle & Ex.10.4 Solutions


Ex.10.4 Part-II


Description: Ex.10.4 Part-II Solution


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