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### Complex plane, Modulus, Argument, Graphical representation of a complex number - Math 102 - diu - swe

• 1. Complex plane, Modulus, Argument, Complex plane, Modulus, Argument, Graphical representation of a Graphical representation of a complex number. complex number. P r e s e n t a t i o n o n Submitted To Mr. Md. Mozammelul Haque Lecturer Department of Software Engineering Daffodil International University
• 2. Section : A ID : 232-35-016 Reduan Ahmad Section : A ID : 232-35-003 Abdullah Al Noman Section : A ID : 232-35-022 Mohammad Ali Nayeem Section : A ID : 222-35-1189 Sabbir Hossen Section : A ID : 232-35-001 Prionti Maliha
• 3. Learning Target: Complex plane Modulus Argument Graphical representation of a complex number.
• 4. Number Line Negative Numbers (−) Positive Numbers (+)
• 5. A plane for complex numbers! 3 units along (the real axis), 4 units up (the imaginary axis). Plot a complex number like 3 + 4i
• 6. Modulus The modulus of a complex number is a fundamental concept in mathematics. The modulus of a complex number is the distance of the complex number from the origin in the the complex plane The modulus of a complex number (z), denoted as |z|, is the non-negative value equal to the square root of the sum of the squares of its real (x) and imaginary (y) parts, expressed as: In this equation, 𝑥 and 𝑦 represent the real and imaginary components of the complex number 𝑧 respectively. When a complex number (z) is plotted on a graph (the complex plane), the distance between the coordinates of the complex number and the origin (0, 0) is called the modulus of the complex number. Modulus of a complex number is always non-negative
• 7. Examples Now lets Find Modulus of |z|=3 + 4i
• 8. Arguments in the Complex Plane complex plane with a vector representing the complex number 3 + 4i
• 9. Argument of Complex Numbers Formula θ = tan⁻¹ (y/x) θ = π - tan⁻¹ |y/x| θ = π + tan⁻¹ |y/x| θ = 2π - tan⁻¹ |y/x|
• 10. Calculating the Argument Be mindful of the quadrant of the complex number to determine the correct value of θ. Formula: For z = x + yi, the argument θ is given by: tan(θ) = y/x θ = arctan(y/x) (using the inverse tangent function)
• 11. Examples Identify: x = 3 and y = 4 Calculate: tan(θ) = 4/3 Solve: θ = arctan(4/3) (using a calculator) Result: θ ≈ 53.13° (first quadrant)
• 13. We can represent complex numbers in the complex plane. We use the horizontal axis for the real part and the vertical axis for the imaginary part.
• 14. Example : The number 3+2𝑗 (where 𝑗=−1​ ) is represented by:
• 15. The point A is the representation of the complex number 3+2𝑗. The horizontal axis is marked R (for the "real" numbered-component), and the vertical axis is marked j (for the imaginary component of the complex number).
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