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Pre-Calc

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Could someone show me how to solve these two problems-I have 10 of each kind to do this weekend and I'm really lost
1. Find product of 8(cos pi/2 + i sin pi/2) * 1/2(cos pi/6 + i sin pi/6)

2. Same problem but find quotient instead of product
Please someone show me these two so I can do my other problems from these examples
Thankyou Thank you

  • Pre-Calc -

    1. That can be written
    8*e^(i*pi/2) * (1/2)e^(i pi/6)
    = 4 e^(2i*pi/3)
    = 4 [cos(2*pi/3) + i sin (2*pi/3)]
    = -2 + 2(sqrt3)i

    2. The quotient is
    16 e^(i*pi/3)
    = 16[cos(pi/3) + i sin(pi/3)]
    = 8 + 8 sqrt3 i

  • Pre-Calc-Pleas recehck -

    Thank you very much for showing me the steps but they don't match my answers that are available: Could you possibly further explain-I'm messed up right now on this concept-
    the answers for Number 1 are
    4cis(2pi/3)
    4cis(pi/3)
    4cis(pi/8)
    4cis(pi/4)
    2. answers for number two are:
    16cis(pi/3)16cis(2pi/3)
    4cis(2pi/3)
    4cis(pi/3)

  • Pre-Calc -

    cis Theta = cos Theta + i sin Theta

    x = r cos Theta
    y = r sin Theta

    so for example
    4 cis 2 pi/3 = 4 cos 2 pi/3 + 4 i sin 2pi/3
    but cos 2p/i/3 = -.5 and sin 2pi/3 = sqrt 3/2
    so
    x = 4 (-.5) = -2
    y = 4 (.5/ sqrt 3) = 2 sqrt3
    -2 + 2 i sqrt 3
    Your answer is the same as that of WLS

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