Find the principal value of the following expressions. Write your answer in the form a + ib.

(a)

(b)

(c)

  (a) -0.266255 -0.963903i

  (b) -1.381098

  (c) -2.156385 +0.273077i

Step-by-step explanation:

A suitable calculator is very handy for such questions. See attached.

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Euler's relation and the definitions of sin and cosh in exponential terms are helpful.

(a)

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(b)

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(c)

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The useful relations are ...

the revenue of the fitness center, y, is the product of two factors: the number of members and the fee paid by each member. there are 320 members now, but number of members goes down by 10 for each $5 increase in fees, so if x is the number of $5 price increases then members is equal to (320 - 10x). since the fee is currently $45, and the fee increases by $5 for every price bump x, the fee is given by (45 + 5x). so, revenue y is given by y = (320 - 10x)(45 + 5x).