Different complex pairs giving same magnitude and phase

1. Is the magnitude of a complex conjugate is always same as the magnitude of its original complex number?
2. How do you find the magnitude and phase of a complex number?
3. Is the argument of the conjugate of a complex number the same?
4. Is the magnitude of a complex number always real?

Is the magnitude of a complex conjugate is always same as the magnitude of its original complex number?

A complex number and its conjugate have the same magnitude: |z|=|z∗|.

How do you find the magnitude and phase of a complex number?

|a + bj| = √a2 + b2. The angle or phase or argument of the complex number a + bj is the angle, measured in radians, from the point 1 + 0j to a + bj, with counterclockwise denoting positive angle. The angle of a complex number c = a + bj is denoted c: c = arctanb/a.

Is the argument of the conjugate of a complex number the same?

We also know that the argument of a complex number equals the negative of the argument of its conjugate.

Is the magnitude of a complex number always real?

ANSWER: Yes. PROOF: Let z = a+bi, where a and b are real numbers.