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Alshia
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Why is the modulus of z, a complex number, |z| = √(a^2+b^2)?
Why is it not |z| = √(a^2+(ib)^2)?
Why is it not |z| = √(a^2+(ib)^2)?
Alshia said:Thank you, [strike]WallsofIvy[/strike] HallsofIvy.
The modulus of a complex number z, denoted as |z|, is the distance between the origin and the complex number in the complex plane. It can also be thought of as the absolute value of the complex number, which is calculated by taking the square root of the sum of the squares of the real and imaginary parts of the complex number.
The magnitude of a complex number, also known as its absolute value, is the same as its modulus. Both terms refer to the distance of the complex number from the origin in the complex plane.
The modulus of a complex number provides important information about the complex number, such as its distance from the origin and its magnitude. It can also be used to calculate the argument or phase angle of the complex number, which gives the direction of the complex number in the complex plane.
To calculate the modulus of a complex number z = a + bi, where a is the real part and bi is the imaginary part, we use the formula |z| = √(a² + b²). This formula is derived from the Pythagorean theorem, where the modulus acts as the hypotenuse of a right-angled triangle with sides a and b.
No, the modulus of a complex number cannot be negative. It is always a positive real number or zero. This is because the modulus represents the distance between the complex number and the origin, and distance cannot be negative.