# How do you find the sum of #8.2+4.4i# from i=1 to 18?

760.6

Assumption: This question means:

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Explanation about some of the method to follow by using an example:
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Consider: 1+2+3 = 6

Hang on to that thought.

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Write expression(1) as:
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We have factored out the 4.4 so all we need to do is sum the values inside the brackets.

Thus the whole thing becomes:

With a calculator:

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To find the sum of ( 8.2 + 4.4i ) from ( i = 1 ) to ( i = 18 ), you can use the formula for the sum of an arithmetic series. The formula is given by:

[ S = \frac{n}{2} \times (a_1 + a_n) ]

where ( S ) is the sum of the series, ( n ) is the number of terms, ( a_1 ) is the first term, and ( a_n ) is the last term.

In this case, ( n = 18 ), ( a_1 = 8.2 + 4.4i ), and ( a_n ) can be calculated using the formula for the ( n )th term of an arithmetic series:

[ a_n = a_1 + (n - 1) \times d ]

where ( d ) is the common difference between consecutive terms. Since the terms are complex numbers, the common difference is ( d = 4.4i ).

Substitute the values into the formulas to find the sum:

[ a_n = (8.2 + 4.4i) + (18 - 1) \times 4.4i ]

[ a_n = 8.2 + 4.4i + 77.6i ]

[ a_n = 8.2 + 81.96i ]

Now, use this value to find ( S ):

[ S = \frac{18}{2} \times (8.2 + (8.2 + 81.96i)) ]

[ S = 9 \times (16.4 + 81.96i) ]

[ S = 147.6 + 737.64i ]

So, the sum of ( 8.2 + 4.4i ) from ( i = 1 ) to ( i = 18 ) is ( 147.6 + 737.64i ).

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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