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Exponential and polar forms of a complex number

Answer

`\text{Exponential form} = sqrt(2)* e^((-1/4*pi)*i)`
`\text{Polar form} (rho , theta) = rho *( cos(theta) + i * sin(theta))`
`rho = sqrt(2)`
`theta = -1/4*pi`
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Allowed: constants, operators and i. For the product, use* Ex: a*b and not ab

This tool converts a complex number from the algebraic format (a + b.i) to its exponential and polar forms.

Graphic representation

z is a complex number represented by the point M on the plane of complex numbers as follows,

graphic-representation-complex-number

Polar form

The polar form of z is written,

`z = r *( cos(\varphi) + i * sin(\varphi))`

r = |z| is the modulus of z.
`\varphi` is the argument of z.

Exponential form

The exponential z format is written,
`z = r * e^(i*\varphi)`

See also

Modulus of a complex number
Argument of a complex number