Add subtract multiply and divide complex numbers

Learning Objectives Add and subtract complex numbers by combining their real and imaginary parts. Multiply complex numbers using the distributive property and the identity i² = -1. Find the complex conjugate of any complex number. Divide complex numbers by multiplying the numerator and denominator by the complex conjugate of the denominator. Simplify expressions involving powers of the imaginary unit, i. Solve multi-step problems involving a combination of addition, subtraction, multiplication, and division of complex numbers. Ever been told you can't take the square root of a negative number? 🤔 It turns out you can, and it opens up a whole new world of numbers with incredible applications! This tutorial covers the fundamental arithmetic operations—addition, subtracti...

TermDefinitionExample Complex Number (Standard Form)A number written in the form a + bi, where 'a' is the real part and 'b' is the imaginary part.5 + 3i (Here, the real part is 5 and the imaginary part is 3). Imaginary Unit (i)The fundamental imaginary number, defined as the principal square root of -1.i = √(-1), which leads to the critical identity i² = -1. Real PartThe component of a complex number that does not have 'i' attached to it.In the complex number -2 + 7i, the real part is -2. Imaginary PartThe coefficient of the imaginary unit 'i' in a complex number.In the complex number -2 + 7i, the imaginary part is 7. Complex ConjugateThe complex conjugate of a complex number a + bi is a - bi. The sign of the imaginary part is flipped.The complex co...

Addition and Subtraction (a + bi) ± (c + di) = (a ± c) + (b ± d)i To add or subtract complex numbers, combine the real parts together and the imaginary parts together, just like combining like terms in algebra. Multiplication (a + bi)(c + di) = (ac - bd) + (ad + bc)i Multiply complex numbers like binomials (using FOIL: First, Outer, Inner, Last). Remember to substitute i² with -1 and then combine like terms. Division \frac{a + bi}{c + di} = \frac{(a + bi)(c - di)}{(c + di)(c - di)} = \frac{(ac + bd) + (bc - ad)i}{c^2 + d^2} To divide, multiply the numerator and the denominator by the complex conjugate of the denominator. This process eliminates the imaginary part from the denominator, similar to rationalizing a radical.