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- The Mandelbrot Set A fractal is a geometric figure that consists of a pattern that is repeated infinitely on a smaller and smaller scale. The most famous fractal is the Mandelbrot Set, named after the Polish-born mathematician Benoit Mandelbrot (19242010). To draw the Mandelbrot Set, consider the sequence of numbers below. c,c2+c,(c2+c)2+c,[ (c2+c)2+c ]2+c,... The behavior of this sequence depends on the value of the complex number c. If the sequence is bounded (the absolute value of each number in the sequence, a+bi=a2+b2 is less than some fixed number N ), then the complex number c is in the Mandelbrot Set, and if the sequence is unbounded (the absolute value of the terms of the sequence become infinitely large), then the complex number c is not in the Mandelbrot Set. Determine whether the complex number c is in the Mandelbrot Set. (a)c=i (b)c=1+i (c)c=2 The figure below shows a graph of the Mandelbrot Set, where the horizontal and vertical axes represent the real and imaginary parts of c, respectively.In how many different ways can two letters be chosen from the letters A, B, C, D, E, F, and G? (The order of the two letters is not important.)License Plate Numbers In a certain state, each automobile license plate number consists of two letters followed by a four-digit number. To avoid confusion between “O” and “zero” and between “I” and “one,” the letters “O” and “I” are not used. How many distinct license plate numbers are possible in this state?