berkeman said:In that kind of problem, you want to get the imaginary numbers out of the denominator. What can you multiply both the top and bottom by, to get rid of the co8mplex denominator?
Benzoate said:zz*=i/6i-3*(-3+6i/-3+6i)=6-3i/(45)=
sqrt((6/45)^2+(3/45)^2)=.15=mag(z)
how would I fine arg(z),Re(z),and Im(z)?
The magnitude of a complex number is the distance from the origin (0,0) on the complex plane to the point representing the complex number. It is also known as the absolute value or modulus of the complex number.
The magnitude of a complex number is calculated using the Pythagorean theorem. It is the square root of the sum of the squares of the real and imaginary parts of the complex number. Mathematically, it can be written as: |a + bi| = √(a² + b²).
No, the magnitude of a complex number is always a positive value. It represents the distance from the origin, and distance cannot be negative.
The magnitude of a complex number is important in understanding the properties of the number. It can be used to calculate the phase angle, conjugate, and inverse of the complex number. It also helps in plotting the number on the complex plane and understanding its relationship with other complex numbers.
The magnitude of a complex number and its argument (phase angle) are related through trigonometric functions. The magnitude is the hypotenuse of a right triangle formed by the real and imaginary parts, while the argument is the angle formed by the hypotenuse and the real axis. They are related by the equation: |z| = √(Re(z)² + Im(z)²) and arg(z) = tan⁻¹(Im(z)/Re(z)).