All categories

2 years ago

Write the complex number 1 +i/1 -i into polar form

Mathematics

1 answer:

IRINA_888 [86]2 years ago

7 0

Answer:

cos(pi/2) + i sin (pi/2)

Step-by-step explanation:

(1+i)/ (1-i)

Multiply top and bottom by (1+i)

(1+i) (1+i)/ (1-i)(1+i)

Foil the top (1+i)(1+i) = 1 +2i +i^2 = 1 +2i -1 = 2i

Foil the bottom ( 1+i)(1-i) = 1 - i^2 = 1 - (-1) =2

2i/2 = i

the magnitude is (0^2+1^2) = 1

The angle is tan^-1( 1/0) = pi/2

cos(pi/2) + i sin (pi/2)

You might be interested in

Point G is the centroid of the right △ABC with m∠C=90° and m∠B=30°. Find AG if CG=4 ft.

o-na [289]

Answer: $\text{Length of AG=}\frac{2\sqrt{63}}{3}$

Explanation:

Please follow the diagram in attachment.

As we know median from vertex C to hypotenuse is CM

$\therefore CM=\frac{1}{2}AB$

We are given length of CG=4

Median divide by centroid 2:1

CG:GM=2:1

Where, CG=4

$\therefore GM=2$ ft

Length of CM=4+2= 6 ft

$\therefore CM=\frac{1}{2}AB\Rightarrow AB=12$

In $\triangle ABC, \angle C=90^0$

Using trigonometry ratio identities

$AC=AB\sin 30^0\Rightarrow AC=6$ ft

$BC=AB\cos 30^0\Rightarrow BC=6\sqrt{3}$ ft

$CN=\frac{1}{2}BC\Rightarrow CN=3\sqrt{3}$ ft

In $\triangle CAN, \angle C=90^0$

Using pythagoreous theorem

$AN=\sqrt{6^2+(3\sqrt{3})^2\Rightarrow \sqrt{63}$

Length of AG=2/3 AN

$\text{Length of AG=}\frac{2\sqrt{63}}{3}$ ft

5 0

2 years ago

I honestly dont know the answer for this

babunello [35]

The picture is blurry

6 0

2 years ago

A forest preserve had 275,301 pine trees. Rangers planted 21,748 new trees. How many trees does the forest preserve have now?

DaniilM [7]

275,301+21,748=297,049

3 0

2 years ago

Read 2 more answers

Which integer is closest to 0 on the number line?

Elenna [48]

The answer is C, 1.
In a number line, the larger number it gets, the more of the right side they're. The smaller the number, the more left side they get.
So, on a number line, 1 is just at the right side of 0, all the other options are at least one more place away from 0.

7 0

3 years ago

Read 2 more answers

1/2x + 3/2 (x + 1) - 1/4 = 5

kompoz [17]

The answer to your problem is x= 15/8 as decimal form it’s 1.875

6 0

2 years ago

Write the complex number 1 +i/1 -i into polar form​

Write the complex number 1 +i/1 -i into polar form