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Consider w = 4(cos(pi/2)+i sin(pi/2) and z=3(cos(3pi/2) +i sin(3pi/2)). What is w +z expressed in polar form?
A. Cos(0) + sin(0)
B. Cos(pi/2)+ isin (pi/2)
C. Cos(pi)+ isin (pi)
D. Cos(3pi/2) +isin (3pi/2)

Answer:

  B. cos(pi/2) +i·sin(pi/2)

Step-by-step explanation:

You can convert to rectangular and back, or you can use the trig function relations directly.

  w = 4·cis(π/2) = 4i

  z = 3·cis(3π/2) = -3i

Then the sum is ...

  w +z = 4i -3i = i = cis(π/2) . . . . matches choice B

__

An alternative representation of z is ...

  z = -3·cis(π/2)

Then ...

  w +z = 4·cis(π/2) -3·cis(π/2) = cis(π/2)

_____

Additional comment

In the above, we have used cis(α) to represent (cos(α) +i·sin(α)).

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