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Complex does not mean complicated. It means the two types of numbers, real and imaginary, together form a complex, just like a building complex (buildings joined together).
In mathematics, a complex number is an element of a number system that extends the real numbers with a specific element denoted i, called the imaginary unit and satisfying the equation =; every complex number can be expressed in the form +, where a and b are real numbers.
complex numbers by adding their real and imaginary parts:-(a+bi)+(c+di)= (a+c)+(b+d)i, (a+bi)−(c+di)= (a−c)+(b−d)i. We can multiply complex numbers by expanding the brackets in the usual fashion and using i2 = −1, (a+bi)(c+di)=ac+bci+adi+bdi2 =(ac−bd)+(ad+bc)i, and to divide complex numbers we note firstly that (c+di)(c−di)=c2 +d2 ...
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A complex number is a number that can be written in the form a + bi a+ bi, where a a and b b are real numbers and i i is the imaginary unit defined by i^2 = -1 i2 = −1. The set of complex numbers, denoted by \mathbb {C} C, includes the set of real numbers \left ( \mathbb {R} \right) (R) and the set of pure imaginary numbers.
The complex numbers $c+di$ and $c-di$ are called complex conjugates. If $z=c+di$, we use $\overline{z}$ to denote $c-di$. Viewing $z=a+bi$ as a vector in the complex plane, it has magnitude $$ |z| = \sqrt{a^2+b^2}, $$ which we call the modulus or absolute value of $z$.
To multiply two complex numbers z1 = a + bi and z2 = c + di, use the formula: z1 * z2 = (ac - bd) + (ad + bc)i. What is a complex number? A complex number is a number that can be expressed in the form a + bi, where a and b are real numbers and i is the imaginary unit, which is defined as the square root of -1.
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To square a complex number, multiply it by itself: multiply the magnitudes: magnitude × magnitude = magnitude 2; add the angles: angle + angle = 2 , so we double them. Result: square the magnitudes, double the angle.
