Java Programming Lab Code

A complex number is represented on polar coordinates to simplify arithmetic operation like multiplication and division on the complex numbers. The complex number's real and imaginary number is converted into polar coordinates' parameter r (radius) and θ (angle/radiant). Complex number on polar coordinates A complex number z = a + ib on polar graph representation is r(cos(θ)+isin(θ)). Here r  - radius , θ  - angle/radiant derived from the complex number c. r  =  |z|  = √ a 2 + b 2   θ   =   atan2  ( b , a ) Complex number on polar form - Multiplication complex number z1 = a + ib z2 = a + ib polar form z1= r1(cos(θ1)+isin(θ1)) z2= r2(cos(θ2)+isin(θ2)) Multiplication z1 x z2 = (r1 x r2)(cos(...

The arithmetic operation like multiplication and division over two Complex numbers is explained Complex number Multiplication multiply two complex numbers z1 and z2. note i^2 = -1 z1 = a + bi z2 = c + di z1*z2 = (a+bi) * (c+di) = a*c + a*di + bi*c + bi*di = a*c + a*di + bi*c + b*d*(i^2) = a*c + a*di + bi*c + b*d*(-1) = a*c + a*di + c*bi - b*d = (a*c - b*d) + (a*di + c*bi) Complex number Division divide two c omplex numbers z1 and z2. note i^2= -1 z1 = a + bi z2 = c + di z1 / z2 = (a+bi ) / (c+di) multiply numerator and denumerator by conjugate z2 conjugate z2 = c + (-1)* di = c - di z1 / z2 = (a+bi) (c-di) / (c+di ) (c-di) (a+bi) (c-di) = a*c - a*di + c*bi -bi*di = a*c - a*di + c*bi -b*d*(i^2) =...

The arithmetic operations addition or subtraction is carried out on the complex numbers by adding or subtracting on respective parts (real and imaginary) of them. Complex numbers Addition Add two complex numbers z1 and z2 z1 = a + bi z2 = c + di z1 + z2 = a + bi + c +di = (a+c) + (b+d)i Complex numbers Subtraction subtract complex numbers z2 from z2 z1 = a + bi z2 = c + di z1 - z2 = (a + bi) - (c+di) = a + bi -c - di = (a-c) + (b-d)i Java code - Complex Addition and Subtraction The following Java codes add and subtract two complex numbers and returns a complex number ,as result of the operation. public class AddSub { public static Complex subtract(Complex C1,Complex C2) { Complex tmp = new Complex(); tmp.real = C1.real - C2.real; tmp.imag = C1.imag - C2.imag; return tmp; } pu...

A complex number consists of two parts; one is the real part and other imaginary part . The real part is marked on x-axis and the imaginary part on the y-axis on the complex plane. A complex number z= a + bi a - Real part b - imaginary part Complex Conjugate A complex numbers can be converted into complex conjugate by simply multiplying (-1) with imaginary parts . It causes the complex point on first quadrant moves to forth quadrant and vice versa. Similarly,the complex point on second quadrant moves to third quadrant and vice versa. Complex z= a +bi conjugate = a + (-1)bi = a - bi Complex - Absolute An absolute value of a complex number is found by the distance between origin and complex number on the complex plane. A complex number = a + bi Absolute value = sqrt ( a^2 + b^2 ) The Java programming code - Complex number The fol...