pre-calculus

solve for z writing the answer in polar form:
#1 z=(3,115 degrees)*(4,290 degrees)

#2 (8,50 degrees)* z=(6,172 degrees)

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  1. Multiply the magnitudes and add the angles to multiply
    This comes from z = x + i y = r e^(i T)
    here we have
    3 e^i 115 * 4 e^i 290

    You know to multiply 3*4 to get 12
    now e^a * e^b = e^(a+b) (rules of exponents)

    so we have 12 e^i(115+290) = 12 e^i 405
    but 405 - 360 = 45
    so we really have
    modulus = 12
    argument = 45 degrees

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  2. (6,172 degrees)
    ----------------
    (8,50 degrees)

    to divide, divide moduli, subtract angles (same discussion as for multiplication)
    (.75) e^i (122)

    by the way, the angles are generally expressed in radians for this notation.

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