Determine the rectangular form of the complex number z= 8(cos (pi/2) + i sin (pi/2)).?

Question

The answer is either...
a) 8 + 8i
b) 8
c) 8i
d) -8i

Need to know how to set up and work a problem like this.

Answer 1

Remember that cos(pi/2) = 0, and sin(pi/2) = 1.

Therefore, if

z = 8(cos (pi/2) + i sin (pi/2)), then
z = 8(0 + i) = 8i

Answer 2

Determine the rectangular form of the complex number z= 8(cos (pi/2) + i sin (pi/2)).?

Just plug in cos(pi/2) = 0 and sin(pi/2) =1, getting:
z = 8(0 + i(1))
z = 8i , so answer is c)

Answer 3

hint: pi/2 radians = 90 degrees. If you don't know the sin and cos of 90 degrees go look them up. Better, though, is to derive them by considering an impossible triangle with two 90 degree angles (draw one as an 88 degree angle and you'll be close enough to see the answer) and then noting that sin = opposite over hypotenuse, and cos = adjacent over hypotenuse [the mnemonic for this and tan is the name of the ancient princess SOHCAHTOA]