complex number
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1. A complex number is an ordered pair of real numbers written in the form a + ib, where a is the real part and b is the imaginary part. 2. Complex numbers combine real and imaginary numbers, extending the real number line to the two-dimensional complex plane with the horizontal axis for real parts and vertical axis for imaginary parts. 3. The fundamental operations of addition, subtraction, multiplication, and division are defined for complex numbers by applying the operations to the real and imaginary parts separately.
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The document provides information on various number system concepts in Vedic maths including:
1. Methods for multiplying numbers with 11, 9, 99, and 999 using place value concepts.
2. Methods for multiplying two-digit and three-digit numbers using the "criss-cross" method.
3. Shortcuts for finding squares and square roots of numbers.
4. Divisibility rules and their applications.
5. Concepts like remainder theorem, power cycles, and unit digit patterns that are useful for solving problems involving remainders and exponents.
6. Information on factors, multiples, and their properties like total number of factors and sum of factors.
Similar to complex number (20)
3.complex numbers Further Mathematics Zimbabwe Zimsec Cambridge
3.complex numbers Further Mathematics Zimbabwe Zimsec Cambridge
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complex number
- 1. 1 Complex Number Name ID No. Md Rasadul Islam 10116034 Mahay Alam Noyon 10116024 Ahasanul Mahbub Jubayer 10116011 Md Rahat Hossain 10116006 Ashraful Alim 10116029 Group Members
- 2. 2 Presented By Md Rasadul Islam
- 3. 3 • An ordered pair of real number generally written in the form “a+ib” • Where a and b are real number and 𝑖 is an imaginary. • In this expression, a is the real part and b is the imaginary part of complex number. Complex Numbers
- 4. When we combine the real and imaginary number then complex number is form. 4 Real Number Imaginary Number Complex Number
- 5. 5 • A complex number has a real part and an imaginary part, But either part can be 0 . • So, all real number and Imaginary number are also complex number.
- 6. 6 Complex number extend the concept of one-dimensional number line to the two-dimensional complex plan. • Horizontal axis use for real part. • Vertical axis for the imaginary part.
- 7. 7(Complex Number) 7 Equations like x2=-1 do not have a solution within the real numbers 12 x 1x 1i 12 i Real no: Imaginary no: Why complex numbers are introduced???
- 8. 8 :then,1-If i 12 i ii 3 14 i ii 5 16 i ii 7 18 i .etc
- 9. 9(Complex Number) i ii )53()12( )51()32( i83 Example Real Axis Imaginary Axis 1z 2z 2z sumz Addition : Complex number added by adding real part in real and imaginary part in imaginary. (a + b𝑖) + (c + d 𝑖) = (a + c) + (b + d) 𝑖. Fundamental Operations with complex number
- 10. (Complex Number) 10 Subtraction: Similarly, subtraction is defined (a + b𝑖) - (c + d 𝑖 ) = (a - c) + (b - d) 𝑖 . i i ii 21 )53()12( )51()32( Real Axis Imaginary Axis 1z 2z 2z diffz 2z Example
- 11. 11(Complex Number) Multiplication: The multiplication of two complex number is define by the following formula: (a + b𝑖).(c + d 𝑖 ) =(ac - bd) + (b c + ad) 𝑖 Square of the imaginary unit is -1. 𝑖²=𝑖 ∗ 𝑖= -1 i i ii 1313 )310()152( )51)(32( Example
- 12. (Complex Number) 12 Division: Division can be defined as: 𝑎 + 𝑏𝑖 𝑐 + 𝑑𝑖 = ( 𝑎𝑐+𝑏𝑑 𝑐²+𝑑² ) + ( 𝑏𝑐−𝑎𝑑 𝑐²+𝑑² )𝑖 EXAMPLE i i 21 76 i i i i 21 21 21 76 22 2 21 147126 iii 41 5146 i 5 520 i 5 5 5 20 i i 4
- 13. Examples of the application of complex numbers: 1) Electric field and magnetic field. 2) Application in ohms law. 3) In the root locus method, it is especially important whether the poles and zeros are in the left or right half planes 4) A complex number could be used to represent the position of an object in a two dimensional plane, (Complex Number) 13 How complex numbers can be applied to “The Real World”???
- 15. 15(Complex Number) FOR YOUR ATTENTION..!