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?
A.) a = sin(θ) and b = cos(θ)
B.) a = cos(θ) and b = sin(θ)
C.) a = rsin(θ) and b = rcos(θ)
D.) a = rcos(θ) and b = rsin(θ)

Answer 1

The equations which can be used to verify the rectangular is a = rcos(θ) and b = rsin(θ)

The correct option is (D)

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)

b = rsin(θ)  

So, the pair of equations used to verify the rectangular form i.e., z = a + bi and the polar form of a complex number is:

a = rcos(θ) & b = rsin(θ).

Learn more about complex number here:

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Answer 2

Answer:

d

Step-by-step explanation:

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