1. EGR 115 Introduction to Computing for Engineers Complex Numbers & 3D Plots – Part 1 Wednesday 05 Nov 2014 EGR 115 Introduction to Computing for Engineers

2. Lecture Outline Wednesday 05 Nov 2014 EGR 115 Introduction to Computing for Engineers Complex Numbers  Complex data & plotting Slide 2 of 16

3. Complex Numbers & 3D Plots Complex Numbers - Introduction Wednesday 05 Nov 2014 EGR 115 Introduction to Computing for Engineers Slide 3 of 16

4. Complex Numbers & 3D Plots Complex Numbers Wednesday 05 Nov 2014 EGR 115 Introduction to Computing for Engineers Imag. Axis Real Axis Slide 4 of 16

5. Complex Numbers & 3D Plots Complex Numbers Wednesday 05 Nov 2014 EGR 115 Introduction to Computing for Engineers Imag. Axis Real Axis Slide 5 of 16

6. Complex Numbers & 3D Plots Complex Numbers Wednesday 05 Nov 2014 EGR 115 Introduction to Computing for Engineers Converting between Polar and Rectangular representations of complex numbers Slide 6 of 16

7. Complex Numbers & 3D Plots Complex Numbers Wednesday 05 Nov 2014 EGR 115 Introduction to Computing for Engineers MATLAB support functions for the manipulation of complex numbers Slide 7 of 16

8. Complex Numbers & 3D Plots Complex Numbers Wednesday 05 Nov 2014 EGR 115 Introduction to Computing for Engineers Adding complex numbers In rectangular format In polar format Much easier in rectangular format Slide 8 of 16

9. Complex Numbers & 3D Plots Complex Numbers Wednesday 05 Nov 2014 EGR 115 Introduction to Computing for Engineers Multiplying complex numbers In rectangular format In polar format Much easier in polar format Slide 9 of 16

10. Complex Numbers & 3D Plots Complex Numbers Wednesday 05 Nov 2014 EGR 115 Introduction to Computing for Engineers In-Class Example:  If your lastname begins with A to M (inclusive) o Develop a function which adds two complex numbers in rectangular format  function c3 = add_rect(c1, c2)  Test your algorithm with: » c1 = 3 – 4i and c2 = 2 + 3i  If your lastname begins with N to Z (inclusive) o Develop a function which multiplies two complex numbers in rectangular format  function c3 = mult_rect(c1, c2)  Test your algorithm with: » c1 = 3 – 4i and c2 = 2 + 3i Compare with: c3 = c1 + c2 Compare with: c3 = c1 * c2 Slide 10 of 16

11. Complex Numbers & 3D Plots Complex Numbers – Relational Operators Wednesday 05 Nov 2014 EGR 115 Introduction to Computing for Engineers Complex Numbers and Relational Operations  Given: c1 = 2 – 4i and c2 = 3 + 3i  What is the value of c1 == c2 ?  What is the value of c1 ~= c2 ?  What is the value of c1 < c2 ? o How do we make this comparison?  MATLAB only uses the real part!!!  This can lead to unexpected results!!! FALSE TRUE Slide 11 of 16

12. Complex Numbers & 3D Plots Complex Numbers – Plotting Wednesday 05 Nov 2014 EGR 115 Introduction to Computing for Engineers Plotting Complex Data  Given the complex function:  Plot y(t) vs 0  t  4  o What did you get? i.e., plot(t, y) Only real part of y was plotted!! Slide 12 of 16

13. Complex Numbers & 3D Plots Complex Numbers – Plotting Wednesday 05 Nov 2014 EGR 115 Introduction to Computing for Engineers Plot both real(y(t)) and imag(y(t)) vs 0  t  4  on the same figure plot(t, real(y), 'b', t, imag(y), 'r') legend('real(y)','imag(y)') Slide 13 of 16

14. Complex Numbers & 3D Plots Complex Numbers – Plotting Wednesday 05 Nov 2014 EGR 115 Introduction to Computing for Engineers Plot real(y(t)) vs imag(y(t)) % Plot real(y(t)) vs imag(y(t)) plot(y) title('Plot of Real(y) vs Imag(y)') xlabel('Real(y)') ylabel('Imag(y)') % Method #2 - A Polar Plot polar(angle(y), abs(y)); title('A Polar Plot of y') Slide 14 of 16

15. Complex Numbers & 3D Plots Complex Numbers – A Quiz Wednesday 05 Nov 2014 EGR 115 Introduction to Computing for Engineers Quiz 8.1  Given  What is the result of: a) x > y b) abs(x) > abs(y) c) real(x) + imag(y) x = 12 + 5i; y = 5 - 13i; TRUE FALSE Slide 15 of 16

16. Next Lecture Wednesday 05 Nov 2014 EGR 115 Introduction to Computing for Engineers 3D Plots Slide 16 of 16