Polar and Rectangular Form
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Let the following graph represent the complex plane (assume that x is the real axis and y is the imaginary axis). Let z=4+3i be the complex number represented by the letter I.
A.
What is the distance from I to the origin? Let α represent this value.
- α=5
- α=2√5
- α=4
- α=3
C.
What are the polar coordinates of the complex number z?
- (4,30.2°)
- (5,36.9°)
- (5,53.1°)
- (4,53.1°)
D.
What is the significance of the answers in parts a and b compared to part c? Choose the best answer.
- They are similar, since the geometry of the complex plane is closely related to the polar coordinates of a complex number.
- They are the same. This is only a phenomenon of the first quadrant though; for a complex number in any other quadrant, these values would be different.
- They are the same, since α represents the modulus of z, and β represents the argument of z.
- Any similarity or equality is pure chance; there is no relationship between these values.