ABCD is a parallelogram. Find the indicated measure:

Use the polar representation to write the following in the form a + bi (a) (-1+ i)^7 (b) (1+v3i)^10

ira [324]

Answer with Step-by-step explanation:

For any complex number x+iy the polar form is represented as

$z=re^{i\theta }$

where

$r^{2}=x^2+y^2\\\\tan(\theta )=\frac{y}{x}$

Part a) x+iy = -1+i

Thus $r=\sqrt{-1^2+1^2}=\sqrt{2}\\\\ \theta _{1}=tan^{-1}(\frac{-1}{1})=\frac{-\pi }{4}$

Thus using De-Morvier's theorem

$(-1+i)^7=(\sqrt{2}e^{i\frac{-\pi }{4}})^7\\\\\therefore (-1+i)^7=2^{7/2}\cdot e^{\frac{i-\pi }{28}}$

Part 2) x+iy = 1+3i

Thus $r=\sqrt{1^2+3^2}=\sqrt{10}\\\\ \theta _{1}=tan^{-1}(\frac{3}{1})=1.25$

Thus using De-Morvier's theorem

$(1+3i)^{10}=(\sqrt{10}e^{1.25i})^{10}\\\\\therefore (1+3i)^{10}=10^{5}\cdot e^{12.5i}$

3 0

3 years ago

Look at the diagram which of the following is a pair of vertical angles

Dafna11 [192]

Where’s the diagram?

8 0

3 years ago

A box is being packed with cubes that measure 1 cubic foot. What is the volume of the box in cubic feet

Nikitich [7]

Answer:

81 cubic foot

Step-by-step explanation:

It is given that the box is packed with cubes whose side is 1 foot. So the volume of one cube is 1 cubic foot.

Now from the figure, we can see that :

Number of cubes fitting the box across its length = 9 cubes

Number of cubes fitting the box across its width = 3 cubes

Number of cubes fitting the box across its height = 3 cubes

And each of these cubes measures 1 x 1 x 1 cubic foot

So the volume of the box can be found out by:

Volume = length x width x height

= 9 x 3 x 3

= 81 cubic foot

Therefore volume of the box is 81 cubic foot.

7 0

3 years ago

James has 30 candies. How many kids (including James) can share these candies evenly? It has to be multiple things, I think.

madreJ [45]

Answer:

So if James has 30 candy it would be best to do it in multiple ways in my opinion, so basically you can divide it among 3 kids including James where the kids get 10 each or you can divide it among 6 kids (still including James) and they all get 5 pieces of candy! Hope this helps and stay safe :)

Step-by-step explanation:

8 0

3 years ago

Read 2 more answers

Liz and Sara are making cookies for a bake sale. The graph shows the number of cookies that Liz bakes during a 5-hour period.

Radda [10]

Statements

case A) Sara had baked more cookies at the start of the $5$ hours than Liz