Question

Question is in the picture, I dont get it.

Answer 1

Answer:

a = 0, b = 1/2

Step-by-step explanation:

Multiplication and division of complex numbers in polar form is pretty simple.

... a·Cis(α) × b·Cis(β) = ab·Cis(α+β) . . . . . multiply magnitudes; add angles

... a·Cis(α) / (b·Cis(β)) = (a/b)·Cis(α-β) . . . divide magnitudes, subtract angles

In your case, you have ...

... 2·Cis(120°) / (4·Cis(30°)) = (2/4)·Cis(120° -30°) = (1/2)·Cis(90°)

Of course, Cis(90°) = cos(90°) +i·sin(90°) = 0 +i.

... (1/2)·Cis(90°) = 1/2·(0 +i) = 0 + 0.5i

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Comment on the use of a calculator

It helps to be aware of how your calculator handles complex numbers. This one can express complex numbers in exponential format, equivalent to a polar form, but requiring specific notation. In this case, the variable D has been assigned the value π/180 so multiplying by it converts degrees to radians. The result of the division is (1/2)i, not 1/(2i).