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4 years ago

PARTA

Mathematics

1 answer:

Vlad [161]4 years ago

3 0

Answer:

21 quizzes

Step-by-step explanation:

Divide 15 by 5 to know how many 5 minutes are in 15 minutes.

$15 \div 5 = 3$

5 minutes are spent for 7 quizzes.

5 × 3 minutes are spent for 7 × 3 quizzes.

$7 \times 3 = 21$

Mrs. Miklos can grade 21 quizzes in 15 minutes.

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3 years ago

Which expression is a cube root of -1+i√3?

Tpy6a [65]

Answer:

<em>The correct option is C.</em>

Step-by-step explanation:

<u>Root Of Complex Numbers</u>

If a complex number is expressed in polar form as

$Z=(r,\theta)$

Then the cubic roots of Z are

$\displaystyle Z_1=\left(\sqrt[3]{r},\frac{\theta}{3}\right)$

$\displaystyle Z_2=\left(\sqrt[3]{r},\frac{\theta}{3}+120^o\right)$

$\displaystyle Z_3=\left(\sqrt[3]{r},\frac{\theta}{3}+240^o\right)$

We are given the complex number in rectangular components

$Z=-1+i\sqrt{3}$

Converting to polar form

$r=\sqrt{(-1)^2+(\sqrt{3})^2}=2$

$\displaystyle tan\theta=\frac{\sqrt{3}}{-1}=-\sqrt{3}$

It's located in the second quadrant, so

$\theta=120^o$

The number if polar form is

$Z=(2,120^o)$

Its cubic roots are

$\displaystyle Z_1=\left(\sqrt[3]{2},\frac{120^o}{3}\right)=\left(\sqrt[3]{2},40^o\right)$

$\displaystyle Z_2=\left(\sqrt[3]{2},40^o+120^o\right)=\left(\sqrt[3]{2},160^o\right)$

$\displaystyle Z_3=\left(\sqrt[3]{2},40^o+240^o\right)=\left(\sqrt[3]{2},280^o\right)$

Converting the first solution to rectangular coordinates

$z_1=\sqrt[3]{2}(\ cos40^o+i\ sin40^o)$

The correct option is C.

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4 years ago