Question

For questions 1-2, compute the modulus and argument of each complex number. Plot and label (with A-G corresponding to 1-2) each complex number in the complex plane given.

1. -2i


2. -5

Answer 1

1. modulus: 2; argument: 3π/2 (radians)

2. modulus: 5; argument: π (radians)

Explanation:

The modulus is the magnitude of the number. When the number is aligned with one of the axes, it is simply the absolute value of the non-zero component. The argument is the arctangent of the imaginary part divided by the real part, with respect given to signs. Again, when the number is aligned with one of the axes, that angle will be some multiple of π/2 radians, where arg(i) = π/2; arg(-1) = π; arg(-i) = 3π/2; arg(1) = 0.

1. the number is aligned with the negative imaginary axis. Its magnitude is |-2| = 2, and its argument is 3π/2.

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2. the number is aligned with the negative real axis. Its magnitude is |-5| = 5, and its argument is π.