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kkurt [141]
3 years ago
13

Write the complex equation 8 + 3i in trigonometric form

Mathematics
1 answer:
Oxana [17]3 years ago
3 0

Answer:

z = 8.544[cos(20.6) + isin(20.6)}

Step-by-step explanation:

Given

8 + 3i

Required

Rewrite in trigonometric form.

The trigonometric form of a complex equation is

z = r[cosθ + isinθ]

Let a = 3 and b = 8

Where

r is calculated by

r² = b² + a²

And

θ is calculated by

θ = arctan(a/b)

Substituting 3 for a and 8 for b

r² = a² + b² becomes

r² = 3² + 8²

r² = 9 + 64

r² = 73

√r² = √73

r = √73

r = 8.544

Calculating θ

θ = arctan(a/b) becomes

θ = arctan(3/8)

θ = arctan(0.375)

θ = 20.556°

θ = 20.6 --- Approximated

Hence, z = r[cosθ + isinθ] becomes

z = 8.544[cos(20.6) + isin(20.6)}

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The straight line distance from the starting point is 41 miles.

<u>Explanation:</u>

Given:

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Distance covered towards east, e = 40 miles

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If we imagine this, then the route forms a right angle triangle

where,

n is the height

e is the base

x is the hypotenuse

Using pythagoras theorm:

(x)² = (n)² + (e)²

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(x)² = 1681

x = 41 miles

Therefore, the straight line distance from the starting point is 41 miles.

5 0
2 years ago
Jackson ran 5/7 of the distance around the school track Sarah around 4/5 of Jackson's distance what fraction of the total distan
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2/3 of the track

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3 years ago
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3 years ago
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Which of the following is a monomial <br><br>A. 5x^2+2x+3<br>B. √x-1<br>C. 4x<br>D. 3/x​
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7 0
3 years ago
How much interest will she earn in 3 years?
alekssr [168]
For this, the equation is 
90× 1.13³=y
X was replaced with y. Since she is gaining, you have to remember she is going to have 100 percent of what he had before, she will not lose any.
90× 1.13= 129.86
Now, we need to find the amount of interest she gained, so we have to subtract 90 from the total.
129.86-90=39.86
We can also find the answer by completing a small chart.
The first column will be the year. The second will be the amount. The third will be the interest for the year.
1                                                90                                                11.7
2                                                101.7                                           13.22
3                                                 114.92                                        14.94
The total would round to 39.86, so her interest for the 3 year would be 39.86, with her having 129.86 altogether.




7 0
3 years ago
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