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Artist 52 [7]
3 years ago
6

Find all complex numbers $z$ such that $z^4 = -4.$

Mathematics
1 answer:
patriot [66]3 years ago
4 0

Converting -4 to polar form gives -4=4\exp(i\pi).

Then the 4th roots of -4 would be the numbers

4^{1/4}\exp\left(i\dfrac{\pi+2k\pi}4\right)

where <em>k</em> is taken from {0, 1, 2, 3}.

So we have

z_1=4^{1/4}\exp\left(\dfrac{i\pi}4\right)=\sqrt2\left(\cos\dfrac\pi4+i\sin\dfrac\pi4\right)=1+i

z_2=\sqrt2\left(\cos\dfrac{3\pi}4+i\sin\dfrac{3\pi}4\right)=-1+i

z_3=\sqrt2\left(\cos\dfrac{5\pi}4+i\sin\dfrac{5\pi}4\right)=-1-i

z_4=\sqrt2\left(\cos\dfrac{7\pi}4+i\sin\dfrac{7\pi}4\right)=1-i

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PLS HELP!! AS SOON AS POSSIBLE !!
Colt1911 [192]
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3 0
3 years ago
William recently purchased a new car for $28,000. The car’s value depreciates 7% each year. What will be the value of the car 5
jarptica [38.1K]

Answer:$18200

Step-by-step explanation:

Find the depreciating price after one year

7% of 28000

7/100* 28000=$1960 is the depreciating cost

Multiple the depreciating cost by 5 year

1960*5=9800

Actual cost - depreciating cost after 5 year

28000-9800= $18200

7 0
3 years ago
Jamie has a half-sheet cake. If she has six friends, how much will each one get?
sesenic [268]

Answer:

<h2>The answer is </h2><h2>B. 1/12</h2>

Step-by-step explanation:

step one:

From the problem state, we can actually conclude that Jamie wants to share the half sheet of cake among her 6 friends

step two:

we can express this problem mathematically as

=\frac{1}{\frac{2}{6} }

we can inverse the denominator and use a multiplication sign instead

\\\\= \frac{1}{2}*\frac{1}{6}

multiplying both denominators we have

\\\\= \frac{1}{12}

The answer is B 1/12

8 0
3 years ago
Helppppppp??????!!!!!!!!!!
zzz [600]
I think the answer would be C. (btw, you should charge your phone/tablet, lol)
7 0
3 years ago
PLEASE I NEED HELP!!!!!!!!
Yanka [14]

Answer:

1) x= 3i, x= - 3i

2) x= +i\sqrt{7}, x = - i

Step-by-step explanation:

1) x^2+9=0

(x+3i)(x-3i)=0

x= 3i, x=-3i

2) x^2-4=-11

x^2=-7

x= ±i\sqrt{7}

x= +i\sqrt{7}, x = - i

hope this helps!! :))

7 0
3 years ago
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