1]Complex Variables & Complex Plane in Hindi - Complex Analysis - Engineering Mathematics

For Complex Analysis, we need basics of Complex Variables and Complex Plane. Complex Numbers: If we combine imaginary term with a real term, we get Complex Numbers. Complex Numbers is always denoted by Z. We can write, Z = x + iy where x and y are real numbers, x is the real part and iy is the imaginary part ( i2 = -1 ) Complex Conjugate: Complex Conjugate of Complex Number is denoted by Z bar. If we reverse the sign of imaginary part, we get Complex Conjugate. If Complex Number is Z = x + iy then Complex Conjugate will be Z = x - iy. If we add Complex Number and its Complex Conjugate, we will get 2x i.e. imaginary part will get cancelled. If we subtract Complex Number and its Complex Conjugate, we will get 2iy. From these equations, we are going to get the value of real part and imaginary point. Real part is x = 1 / 2 [ z + z bar ] Imaginary part is x = 1 / 2 [ z - z bar ] Complex Plane: It is a geometrical representation of complex numbers as points in the plane. It is the Cartesian coordinate system. The complex number is a 2D vector so, in the complex plane, a complex number is always denoted by a vector. Polar form: For polar coordinate system, the value of real part and imaginary part are x = rcos(theta) and y = rsin(theta) respectively. The magnitude of z: The magnitude of z is denoted by the modulus of z or r. The magnitude of z is given as root of real part square + imaginary part square. The angle of z: The angle of z is also called an argument of z or amplitude of z and is denoted as arg and amp. Arg (z) or theta is equal to a tan inverse of imaginary part divided by real part. Check out the video tutorial for the more better explanation.