Operations with complex numbers are by no means limited just to addition, subtraction, multiplication, division, and inversion, however. These are the basic operations you will need to know in order to manipulate complex numbers in the analysis of AC circuits. To obtain the reciprocal, or “invert” (1/x), a complex number, simply divide the number (in polar form) into a scalar value of 1, which is nothing more than a complex number with no imaginary component (angle = 0): When multiplying complex numbers in polar form, simply multiply the polar magnitudes of the complex numbers to determine the polar magnitude of the product, and add the angles of the complex numbers to determine the angle of the product:ĭivision of polar-form complex numbers is also easy: simply divide the polar magnitude of the first complex number by the polar magnitude of the second complex number to arrive at the polar magnitude of the quotient, and subtract the angle of the second complex number from the angle of the first complex number to arrive at the angle of the quotient: Multiplication and Division of Complex Numbers in Polar Formįor longhand multiplication and division, polar is the favored notation to work with. When subtracting complex numbers in rectangular form, simply subtract the real component of the second complex number from the real component of the first to arrive at the real component of the difference, and subtract the imaginary component of the second complex number from the imaginary component of the first to arrive the imaginary component of the difference: For addition, simply add up the real components of the complex numbers to determine the real component of the sum, and add up the imaginary components of the complex numbers to determine the imaginary component of the sum: Addition and Subtraction of Complex Numbers in Rectangular FormĪddition and subtraction with complex numbers in rectangular form is easy. It will make your study of AC circuit much more pleasant than if you’re forced to do all calculations the longer way. It is highly recommended that you equip yourself with a scientific calculator capable of performing arithmetic functions easily on complex numbers. Some scientific calculators are programmed to directly perform these operations on two or more complex numbers, but these operations can also be done “by hand.” This section will show you how the basic operations are performed. The basic laws of algebra are the Commutative Law For Addition, Commutative Law For Multiplication, Associative Law For Addition, Associative Law For Multiplication, and the Distributive Law.Since complex numbers are legitimate mathematical entities, just like scalar numbers, they can be added, subtracted, multiplied, divided, squared, inverted, and such, just like any other kind of number.Meaning, whatever operation is being used on one side of equation, the same will be used on the other side too. The golden rule of algebra states Do unto one side of the equation what you do to others.The basic rules of algebra are the commutative, associative, and distributive laws.The basics of algebra are the commutative, associative, and distributive laws.Then, solve the equation by finding the value of the variable that makes the equation true. To solve an algebraic expression, simplify the expression by combining like terms, isolate the variable on one side of the equation by using inverse operations. How do you solve algebraic expressions?.
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