Ask question

Ask question

All categories

valentina_108 [34]

3 years ago

11

NEED HELP ! 20 POINTS

1 answer:

prohojiy [21]3 years ago

8 0

If $z=1-i$ , then $|z|=\sqrt{1^2+(-1)^2}=\sqrt2$ and $\arg z=-\dfrac\pi4$ because $z$ lies in the fourth quadrant.

By DeMoivre's theorem,

$z=|z|e^{i\arg z}\implies z^{10}=(\sqrt2)^{10}e^{-i10\pi/4}=32e^{-i5\pi/2}=32e^{-i\pi/2}=-32i$

so the answer is B.

You might be interested in

A dump truck delivers dirt for $6 per cubit foot. The dimensions are 4 3/4 ft by 8 ft by 17 ft. How much does a full load of d

schepotkina [342]

Answer:

None. There can't be any dirt in it because it's a hole.

Step-by-step explanation:

3 0

3 years ago

Scott sells tie-dyed T-shirts for $15 each.Each T-shirts cost him $5 to make.He also has $100 in fixed costs per year for his T-

sergeinik [125]

He has to sell 60 t-Shirts. if you need the work message me :D

3 0

4 years ago

The greatest common factor (GCF) of x^3, x^7, x^9 is ?<br> Please help

solong [7]

Answer:

$x^3$

Step-by-step explanation:

Let the greatest common factor of $a,b,c$ such that $a,b,c \in\mathbb{Z}$ and they are not all equal to zero, $d$ is the common divisor of $a$ and $b$ . Therefore, $d \mid a$ and $d \mid b$

You can write

$D(a) = \{d \in\mathbb{Z} : d \mid a\}$

$D(b) = \{d \in\mathbb{Z} : d \mid b\}$

The greatest common factor of $a,b$ is given as

$D(a,b) = \{d \in\mathbb{Z} : d \mid a \text{ and } d \mid b\}$

and

$D(a, b) = D(a) \cap D(b)$

This happens because $D(a,b)$ is upper bounded because if $a\neq 0$ then $d \leq |a|$

for all $d\in D(a, b)$ . Therefore, the set $D(a, b)$ has the greatest elements.

Taking $x^3, x^7, x^9$ such that $x>0$

You can note that $x^7 = x^3 \cdot x^4$ and $x^9 = x^3 \cdot x^6 = x^3 \cdot x^3 \cdot x^3$

Therefore, the greatest common factor is $x^3$

Note: $x^3 \cap x^7 \cap x^9 = x^3$

6 0

3 years ago

Two hundred dollars is increased by 25% and the result decreased by 25%

erastova [34]

Answer:

If $200 increased by 25%, your result would be $250

If it then decreased by 25%, your result would be $187.5

Step-by-step explanation:

Multiply 200 and 25% and add 200 to get 250

Multiply 250 and 25% and then add that value to get 187.5

5 0

3 years ago

Read 2 more answers

Need help asap will give brainly

TiliK225 [7]

Answer:

angle 1 and 8 - alternate exterior

6 and 7 - vertical angles

8 and 4 - corresponding

3 and 6 - alternate interior

1 and 5 - corresponding

8 0

3 years ago