Can the division expression 4 divided by 15 be shown as a fraction?

which expression represents purely real numbers and which expression represents non-real complex number?

Ray Of Light [21]

Incomplete question. However, I provided some explanation about non-real complex numbers.

<u>Explanation</u>:

In Mathematics, the term complex numbers (non-real complex numbers) in simple terms refers to numbers that containing an imaginary addition to it.

For example, the numbers 3i, 3 + 5i, 3i/4 are <u>non-real numbers</u> because of the addition of an imaginary part which is denoted by 'i'.

While real numbers, on the other hand, are numbers that do not include an imaginary part; they stand on their own, such as whole numbers 0, 1, 2, 3, etc, rational numbers like 3/4, etc.

5 0

3 years ago

(7 + 7i)(2 − 2i)

Ostrovityanka [42]

The complex number -7i into trigonometric form is 7 (cos (90) + sin (90) i) and 3 + 3i in trigonometric form is 4.2426 (cos (45) + sin (45) i)

<h3>What is a complex number?</h3>

It is defined as the number which can be written as x+iy where x is the real number or real part of the complex number and y is the imaginary part of the complex number and i is the iota which is nothing but a square root of -1.

We have a complex number shown in the picture:

-7i(3 + 3i)

= -7i

In trigonometric form:

z = 7 (cos (90) + sin (90) i)

= 3 + 3i

z = 4.2426 (cos (45) + sin (45) i)

$\rm 7\:\left(cos\:\left(90\right)\:+\:sin\:\left(90\right)\:i\right)4.2426\:\left(cos\:\left(45\right)\:+\:sin\:\left(45\right)\:i\right)$

$\rm =7\left(\cos \left(\dfrac{\pi }{2}\right)+\sin \left(\dfrac{\pi }{2}\right)i\right)\cdot \:4.2426\left(\cos \left(\dfrac{\pi }{4}\right)+\sin \left(\dfrac{\pi }{4}\right)i\right)$

$\rm 7\cdot \dfrac{21213}{5000}e^{i\dfrac{\pi }{2}}e^{i\dfrac{\pi }{4}}$

$\rm =\dfrac{148491\left(-1\right)^{\dfrac{3}{4}}}{5000}$

=21-21i

After converting into the exponential form:

$\rm =\dfrac{148491\left(-1\right)^{\dfrac{3}{4}}}{5000}$

From part (b) and part (c) both results are the same.

Thus, the complex number -7i into trigonometric form is 7 (cos (90) + sin (90) i) and 3 + 3i in trigonometric form is 4.2426 (cos (45) + sin (45) i)

Learn more about the complex number here:

brainly.com/question/10251853

#SPJ1

3 0

2 years ago

Evaluate.<br> 2 • 9 – 1 =

Nostrana [21]

Answer:

17

Step-by-step explanation:

You have to multiply 2 and 9 first, so the product is 18. Now you have to subtract that from 1 itself and therefore, the final answer is 17.

Hope this helps you!?!

8 0

3 years ago

3. Ravi is covering a table top in mosaic tiles that

Zinaida [17]

Answer:

432 tiles

Step-by-step explanation:

First, convert the dimensions of the table to inches.

There are 12 inches in a foot, so multiply 1.5 and 2 by 12.

1.5(12) = 18

2(12) = 24

So, the dimensions of the table in inches are 18 by 24.

Find the area of the table using the formula, A = lw

A = lw

A = (18)(24)

A = 432

So, the area is 432 square inches.

Since each tile is one square inch, the table will fit 432 of these.

So, Ravi will need 432 tiles.

7 0

3 years ago

B) In a sunny day, the length of the shadow of a pole 30m long is equal to the

KiRa [710]

When the shadow is 30 meters long, the angle of the sun is 45°.

When the shadow is 51.96 meters long, the angle of the sun is arctan(30/51.96) = 30°

7 0

3 years ago

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