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 22 = -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) + ib+d), Subtraction Rule: (a + ib) - (c+ id) = (a -c) + ib - d), Multiplication Rule: (a + ib) +(c + id) = (ac - bd) +i(ad + bc), Division Rule: (a + ib)/(c+id) = ((ac+bd) +i(bc - ad))/(e? + d), The complex conjugate of the complex number a + ib is given as a - ib, The polar form of a complex number z = +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 (vey+z) @= if 2>0,4 +0 if :