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3 years ago

If Z= 2+2i, what is z^4?

Mathematics

2 answers:

ira [324]3 years ago

8 0

Answer:

D. 64 (cos(pi)+isin(pi))

Step-by-step explanation:

Put 2+2i into trigonometric form, raise the r value to the power of 4, and multiply the angle value (theta) by 4 to get the equation of z^4. In this case, r was 2(sqrt2), which raised to the 4th power was 64. The angle value was pi/4, which multiplied by 4 was pi. That's how we get the answer:

64 (cos(pi)+isin(pi)). How this helps!

Dimas [21]3 years ago

7 0

Answer:

assume z is equal to 5.

log(z^4/5) equals log(5^4/5) equals log(5^3) equals 2.096910013.

4 * log(5) - log(5) equals 2.096910013.

they give you the same answer.

this means they're equivalent.

Step-by-step explanation:

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3 years ago

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Using the provided measures determine the measure of angle K.

forsale [732]

Answer:

B. 34.90°

Step-by-step explanation:

✔️First, find GF using Trigonometric function:

Reference angle = 58°

Adjacent length = GF

Hypotenuse = 6 cm

Apply CAH, thus:

Cos 58 = Adj/Hyp

Cos 58 = GF/6

GF = 6*Cos 58

GF = 3.17951558 ≈ 3.18 cm

✔️Find angle K using the Sine Rule:

$\frac{sin(K)}{GF} = \frac{sin(G)}{KF}$

Substitute

$\frac{sin(K)}{3.18} = \frac{sin(64)}{5}$

Multiply both sides by 3.18

$sin(K) = \frac{sin(64)}{5}*3.18$

$sin(K) = 0.5716$

$K = sin^{-1}(0.5716)$

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3 years ago

Solve for x and y. 4x-3y=16 -2x+4y=-2 DUE 2/7/17!

Trava [24]

$\left \{ {{4x-3y=16\:(I)} \atop {-2x+4y=-2\:(II)}} \right.$

Multiply the 2nd equation by (-4). This will eliminate the x's when you add the two new equations together.
 $\left \{ {{4x-3y=16\:\:\:\:\:\:\:\:\:\:} \atop {-2x+4y=-2\:*(-4)}} \right.$
$\left \{ {{\diagup\!\!\!\!4x-3y=16} \atop {-\diagup\!\!\!\!4x+8y=-4}} \right.$
--------------------
$5y = 12$
$\boxed{\boxed{y = \frac{12}{5}}}\end{array}}\qquad\quad\checkmark$

Let's replace the value found in the first equation:
$4x-3y=16\:(I)$
$4x-3*( \frac{12}{5}) =16$
$4x - \frac{36}{5} = 16$
least common multiple (5)
$\frac{20x}{\diagup\!\!\!\!5} - \frac{36}{\diagup\!\!\!\!5} = \frac{80}{\diagup\!\!\!\!5}$
$20x - 36 = 80$
$20x = 80 + 36$
$20x = 116$
$x = \frac{116}{20} \frac{\div4}{\div4} \to\: \boxed{\boxed{x = \frac{29}{5} }}\end{array}}\qquad\quad\checkmark$

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4 years ago

A standard deck of cards is made up of four suits: diamonds, spades, hearts, and clubs. What is the probability that you draw a

Oksi-84 [34.3K]

Answer:

1/2, because there's 4 suits, and so the probability of choosing 2 is 1/2.

Step-by-step explanation:

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3 years ago