• Imaginary
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• Polar
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Modulus of a Complex Number

The modulus of a complex number is the length of the vector determined by the origin of its coordinates and affix. It is denoted by |z|.

Argument of a Complex Number

The argument of a complex number is the angle that forms the vector with the real axis. It is denoted by arg(z).

Expression of a Complex Number in Polar Form

z = r_α

|Z| = r r is the modulus.

arg(z) = is the argument.

Examples

Express in polar form:

z = 2_60º

z = 2_120º

z = 2_240º

z = 2_300º

Z = 2

z = 2_0º

Z = −2

z = 2_180º

Z = 2i

z = 2_90º

Z = −2i

z = 2_270º

Trigonometric form

r_α = r (cos α + i sin α)

Examples

z = 2_120º

z = 2 · (cos 120º + i sin 120º)

z =1_0º = 1

z =1_180º = −1

z =1_90º = i

z =1_270º = −i

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