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Misha Larkins [42]
3 years ago
10

For z = 2cis 60°, find z4 in rectangular form.

Mathematics
2 answers:
a_sh-v [17]3 years ago
5 0
By DeMoivre's theorem,

z=2\mathrm{cis}60^\circ\implies z^4=2^4\mathrm{cis}(4\times60)^\circ=16\mathrm{cis}\,240^\circ
z^4=16(\cos240^\circ+i\sin240^\circ)
z^4=16\left(-\dfrac12-i\dfrac{\sqrt3}2\right)
z^4=-8-i8\sqrt3
REY [17]3 years ago
5 0

Answer:

For plato users the answeris -8-8\sqrt{3i}

Step-by-step explanation:

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1) Draw the arrow diagram and the matrix representation for the relation: R={(1, 2), (3, 4), (2, 3), (3, 2), (2, 1), (3, 1), (4,
tensa zangetsu [6.8K]

Answer:

The arrow diagram and the matrix representation for the relation is shown below.

Step-by-step explanation:

The given relation is

R={(1, 2), (3, 4), (2, 3), (3, 2), (2, 1), (3, 1), (4, 3)}

If a relation is defined as

R=\{(x,y)|x\in R,y\in R\}

Then the set of x values is domain and set of y values is range.

The domain of the function is

Domain={1, 2, 3, 4)

The range of the function is

Range={1, 2, 3, 4)

In arrow diagram, we have two sets first set represents the domain and second set represents the range. The arrow connecting the element represent the relation.

In matrix representation,

M_{ij}=\begin{cases}1 & \text{ if } (x_i,y_j)\in R \\ 0 & \text{ if } (x_i,y_j)\notin R\end{cases}

The arrow diagram and the matrix representation for the relation is shown below.

6 0
3 years ago
2 apples plus 2 apples
anyanavicka [17]

Answer:

4 apples

Step-by-step explanation:

2 + 2 = 4

Hope this helps!

Good Luck!

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7 0
3 years ago
Read 2 more answers
A student makes a sign out of a rectangular piece of cardboard for an upcoming event at school. The piece of cardboard has a len
seraphim [82]

Answer:

915 in²

Step-by-step explanation:

The area of the rectangle :

Length = 32 inches

Width = 25 - (10+10) = 25 - 20 = 5 inches

Area of rectangle = Length * width

Area = 32 * 5 = 160 in²

Area of triangle :

Base = 25 inches

Height = (46 - 32) inches = 14 inches

Area of triangle = 1/2 * base * height

Area of triangle = 1/2 * 25 * 14 = 175 in²

Total area = (160 + 175)in² = 335 in²

Total area of cardboard :

50 inches * 25 inches = 1250 in²

Amount of cardboard not used :

(1250 - 335) in² = 915 in²

3 0
3 years ago
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dlinn [17]
We shall take X as the total amount of cash her piggy bank can hold
therefore 1x/10+400=1x/2
400=1x/2-1x/10
we should make the denominator's the same
400=5x/10-1x/10
400=4x/10
400*10=4x
4000=4x
4000/4=X
1000=X
hope u found this useful
4 0
3 years ago
The question and options are in the picture. PLEASE HELP FAST!!!
algol13
D) they will all change by the same amount
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