Add and subtract complex numbers

Learning Objectives Identify the real and imaginary parts of a complex number. Add two or more complex numbers by combining their corresponding real and imaginary parts. Subtract complex numbers by distributing the negative sign and combining like terms. Simplify expressions involving multiple additions and subtractions of complex numbers. Solve simple algebraic equations for an unknown complex number. Represent the addition and subtraction of complex numbers graphically as vector operations on the complex plane. Ever wondered how engineers model AC circuits or how physicists describe quantum states? 🤔 They use complex numbers, and the first step is learning their basic arithmetic! This tutorial covers the fundamental operations of adding and subtracting complex numbers. M...

TermDefinitionExample Complex NumberA number written in the standard form `z = a + bi`, where 'a' and 'b' are real numbers, and 'i' is the imaginary unit.The number `5 - 3i` is a complex number where `a = 5` and `b = -3`. Imaginary Unit (i)The fundamental imaginary number defined by the property `i^2 = -1`, or equivalently, `i = \sqrt{-1}`.`i` allows us to find solutions to equations like `x^2 + 1 = 0`. Real PartFor a complex number `z = a + bi`, the real part is the real number 'a'. It is denoted as `Re(z)`.For `z = -7 + 2i`, the real part is `Re(z) = -7`. Imaginary PartFor a complex number `z = a + bi`, the imaginary part is the real number 'b' that multiplies the imaginary unit 'i'. It is denoted as `Im(z)`.For `z = -7 + 2i`,...

Addition of Complex Numbers If `z_1 = a + bi` and `z_2 = c + di`, then `z_1 + z_2 = (a + c) + (b + d)i` To add complex numbers, simply add the real parts together and add the imaginary parts together. This is analogous to combining like terms in polynomial algebra. Subtraction of Complex Numbers If `z_1 = a + bi` and `z_2 = c + di`, then `z_1 - z_2 = (a - c) + (b - d)i` To subtract complex numbers, subtract the real parts and subtract the imaginary parts. Be careful to distribute the negative sign to both the real and imaginary parts of the number being subtracted.