Question

Which pair of equations can be used to verify the rectangular form, z = a + bi, and the polar form of a complex number are equivalent?

Answer 1

The equations which can be used to verify the rectangular form (z = a + bi) and the polar form of a complex number are equivalent is a = rcos(θ) and b = rsin(θ)

How to transform polar coordinates to rectangular coordinates?

In geometry, the relationship between a polar coordinate (r, θ) and a rectangular coordinate (x, y) based on the conversion rules is given by the following polar functions:

a = rcos(θ)    ....equation 1.

b = rsin(θ)     ....equation 2.

Where:

• θ is the angle.

• r is the radius of a circle.

In conclusion, the pair of equations which can be used to verify the rectangular form (z = a + bi) and the polar form of a complex number are equivalent is:

a = rcos(θ) and b = rsin(θ).

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