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Juliette [100K]
2 years ago
5

Using De-Moivre's theorem, prove that i^2= -1.​

Mathematics
1 answer:
Novosadov [1.4K]2 years ago
3 0

Write i in trigonometric form. Since |i| = 1 and arg(i) = π/2, we have

i = exp(i π/2) = cos(π/2) + i sin(π/2)

By DeMoivre's theorem,

i² = exp(i π/2)² = exp(i π) = cos(π) + i sin(π)

and it follows that i² = -1 since cos(π) = -1 and sin(π) = 0.

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A big lockers above a smaller locker they both have 0.5 m wide and 0.6 m deep Big lockers 1.2 m tall and small lockers half of t
Tomtit [17]

Answer:

0.54\,\,m^3

Step-by-step explanation:

Given: Dimensions of a big locker are 0.5 m × 0.6 m × 1.2 m

Dimensions of a small locker are 0.5 m × 0.6 m × \frac{1.2}{2}=0.6\,\,m (as height of small locker is half the height of big locker )

To find: total volume of one big locker and one small locker

Solution:

Volume of cuboid = length × breadth × height

Total volume of one big locker and one small locker = Total volume of one big locker + total volume of one small locker

= 0.5\times 0.6\times 1.2+0.5\times 0.6\times 0.6

=0.5\times 0.6\left ( 1.2+0.6 \right )\\=0.3(1.8)\\=0.54\,\,m^3

4 0
3 years ago
Read 2 more answers
I need to know the surface area of these
anastassius [24]

9514 1404 393

Answer:

  245 cm²

Step-by-step explanation:

The surface area of a cone is given by ...

  SA = πr(r +s) . . . . where r is the radius, and s is the slant height

Filling in the given values, we have ...

  SA = (3.14)(3 cm)(3 cm +23 cm) = (3.14)(3)(26) cm² ≈ 245 cm²

The surface area of the cone is about 245 cm².

6 0
2 years ago
How many solutions does the equation have? 5(w−1)−2=5w+7<br><br>A.0 B.1 C.infinitely many
bogdanovich [222]
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6 0
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A=1/2bh

1/2bh=A

1/2bh÷1/2bh=A÷1/2bh (the 1/2b will cancel with the 1/2b on the left leaving h)

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Alenkinab [10]
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