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Answer:
The arc length of the semicircle is or
Step-by-step explanation:
The complete question in the attached figure
we know that
The circumference of a semicircle is given by the formula
where
D is the diameter of the semicircle
we have
substitute
----> exact value
Assume
----> approximate value
therefore
The arc length of the semicircle is or
Z = a + bi
z = 4 + 4i
r² = a² + b²
r² = (4)² + (4)²
r² = 16 + 16
r² = 32
r = 4√(2)
r = 4(1.414)
r = 5.656
z = a + bi
z = rcosθ + (rsinθ)i
z = r(cosθ + i sinθ)
z = 4 + 4i
z = 5.656cosθ + (5.656sinθ)i
z = 5.656(cosθ + i sinθ)
z = 5.656(cos45 + i sin45)
The polar form of 4 + 4i is approximately equal to 5.656(cos45 + i sin45).
z = 4 + 4i
r² = a² + b²
r² = (4)² + (4)²
r² = 16 + 16
r² = 32
r = 4√(2)
r = 4(1.414)
r = 5.656
z = a + bi
z = rcosθ + (rsinθ)i
z = r(cosθ + i sinθ)
z = 4 + 4i
z = 5.656cosθ + (5.656sinθ)i
z = 5.656(cosθ + i sinθ)
z = 5.656(cos45 + i sin45)
The polar form of 4 + 4i is approximately equal to 5.656(cos45 + i sin45).