Please I need help with questions number 1 and 4. Thank you

Mosta Profe D 9 9 1.) Consider the complex number z = -1 + 3i. What is the value of |z|2 = z* . z ? Plot this number in the complex plane (y-axis = Im, x-axis = Re). If we rewrite z in the form z = Ael, what is the value of A? What is the value of 0? What is leto |? 2.) Given matrices A = ( 21) and B = ( 2), what is their product: A . B =? 3 3.) Find J_2(x - 3)8(x - 4)dx, explaining clearly (i.e., use words). ["8" is the Dirac delta function.] 4.) Sketch a graph of the function y(x) = 2e ( vs. x for c=5. Indicate the x and y scales. Is the function symmetric? What is the limit for x - too? What is the significance of c in the exponent? What is the relation between a photon's wavelength, 2, and frequency, f? Roughly what wavelength does a radio wave for station 99.9 on the FM dial have (i.e., the frequency is 99.9 MHz)? Atomic sizes are on the order of Angstroms, A, where 1A = 10-10m. What is the frequency of a photon of wavelength 1 = 0.1 A? 6.) Write down an equation describing a sinusoidal traveling wave (in 1-D). Tell us (words and/or equations) what in your equation tells us the speed and direction of the wave? [Hint: you can google this if you do not know the answer. Be sure you understand it though!] 7.) What does it mean for two functions to be "orthogonal"? Then, give a specific example of two orthogonal functions. V/ = Recu - Hz 5 s 0 . 0 m 1 = m S