Exercise 1. (10 points] A complex number is a number that can be expressed in the form a +ib, where a and b are real numbers, and i is a solution of the equation x2 = -1. Because no real number satisfies this equation, i is called an imaginary number. For the complex number a +ib, a is called the real part, and b is called the imaginary part. When performing the arithmetic operations on complex numbers, remember to combine "similar" terms, i.e., the real and the imaginary parts. For two complex numbers a + ib and c+ id, the following operations are defined as follows: Addition Rule: (a + ib) +(c + id) = (a + c) + i(b + d), Subtraction Rule: (a + ib) - (c+id) = (a c) + i(b - d), Multiplication Rule: (a + ib) * (c+ id) = (ac bd) + iad + bc), Division Rule: (a + ib)/(c + id) = (ac+bd) +i(bc - ad))/(c2 +d2), The complex conjugate of the complex number a + ib is given as a - ib, The polar form of a complex number z = x + iy can be written as z = r cis 0, where p= x2 + y2 is the magnitude of the complex number, and is the phase of z and given as follows: = (2arctan ( Voz yet +1 0= if x > 0,7 +0 if :