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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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Answer:

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Step-by-step explanation:

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Step-by-step explanation:

Given: Weight of Blue whale = 3\times10^5\text{ pounds}

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Number of times blue whale's weight  is heavier than the narwhal's weight = =\dfrac{\text{Weight of Blue whale}}{\text{Weight of Narwhal }}

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<em>simplify </em>

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<em>add 5 to both sides </em>

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<em>simplify </em>

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<em>divide both sides by 5 </em>

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<em> </em>

<em />

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Step-by-step explanation:

Detailed explanation and calculation is shown in the image below

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