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)=(ac)+i(bd), - Multiplication Rule: (a+ib)(c+id)=(acbd)+i(ad+bc), - Division Rule: (a+ib)/(c+id)=((ac+bd)+i(bcad))/(c2+d2), - The complex conjugate of the complex number a+ib is given as aib, - The polar form of a complex number z=x+iy can be written as z=r cis , where r=x2+y2 is the magnitude of the complex number, and is the phase of z and given as follows: =2arctan(x2+y2+xy)undefinedifx>0,y=0ifx