Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

15 i*(-i-1)=
Your answer should be a complex number in the form
a+bi where
a and
b are real numbers.

$15 i \cdot(-i-1)=$ $\newline$ Your answer should be a complex number in the form $a+b i$ where $a$ and $b$ are real numbers.

View step-by-step help

View step-by-step help

Write equations of cosine functions using properties

Full solution

Q.

15 i \cdot(-i-1)=

\newline

Your answer should be a complex number in the form

a+b i

where

a

and

b

are real numbers.

Multiply complex numbers: Multiply the complex numbers $15i$ and $(-i - 1)$ . We distribute $15i$ across the terms in the parentheses. $15i \times (-i) + 15i \times (-1)$
Distribute $15i$ : Calculate the product of $15i$ and $-i$ . $\newline$ The product of $i$ and $-i$ is $-i^2$ . Since $i^2 = -1$ , $-i^2 = 1$ . $\newline$ $15i \cdot (-i) = 15 \cdot 1 = 15$
Calculate product of $15i$ and $-i$ : Calculate the product of $15i$ and $-1$ . $\newline$ The product of $i$ and $-1$ is $-i$ . $\newline$ $15i \times (-1) = -15i$
Calculate product of $15i$ and $-1$ : Combine the results from Step $2$ and Step $3$ . $\newline$ $15$ (from Step $2$ ) + ( $-15i$ ) (from Step $3$ )
Combine results from Step $2$ and Step $3$ : Write the final answer in the form $a+bi$ . $\newline$ The real part $a$ is $15$ , and the imaginary part $b$ is $-15$ . $\newline$ So, the final answer is $15 - 15i$ .

More problems from Write equations of cosine functions using properties

Question

Find an equation for a sinusoidal function that has period

2\pi

1

, and contains the point

\left(\pi, -1\right)

\newline

Write your answer in the form

f(x)=A\cos(Bx+C)+D

A

B

C

D

are real numbers.

\newline

f(x)=

Posted 7 months ago

Question

Find an equation for a sinusoidal function that has period

2\pi

1

, and contains the point

\left(-\frac{\pi}{2},-1\right)

. Write your answer in the form

f(x) = A\sin(Bx + C) + D

A

B

C

D

are real numbers. `f(x)` =______

Posted 9 months ago

Question

Find an equation for a sinusoidal function that has period

2\pi

1

, and contains the point

(0,-1)

\newline

Write your answer in the form

f(x) = A\cos(Bx + C) + D

A

B

C

D

are real numbers.

\newline

f(x) =

Posted 8 months ago

Question

Franklin Middle School is having a canned food drive. In Mr. Lao's class, Mr. Lao brought

10

cans of food, and each student brought

2

cans. In Ms. Roger's class, Ms. Rogers did not bring any cans, but each student brought

3

cans of food. Write two equations in slope-intercept form to represent the number of cans of food for each class

y

in terms of the number of students

x

Posted 8 months ago

Question

Franklin Middle School is having a canned food drive. In Mr. Lao's class, Mr. Lao brought

10

cans of food, and each student brought

2

cans. In Ms. Roger's class, Ms. Rogers did not bring any cans, but each student brought

3

cans of food. Write two equations in slope-intercept form to represent the number of cans of food for each class

y

in terms of the number of students

x

Posted 8 months ago

Question

Kris is wrapping Christmas lights around the railing that runs around three sides of his square porch If one side of his porch is

12

feet long, and each strand of his Christmes lights will wrap around a

70

-inch length of the railing, what is the minimum number of strands Kris needs to completely wrap the porch railing?

\newline

6

\newline

7

\newline

8

\newline

9

Posted 8 months ago

Question

Kris is wrapping Christmas lights around the railing that runs around three sides of his square porch If one side of his porch is

12

feet long, and each strand of his Christmas lights will wrap around a

70

-inch length of the railing, what is the minimum number of strands Kris needs to completely wrap the porch railing?

\newline

6

\newline

7

\newline

8

\newline

9

Posted 8 months ago

Question

For a given input value

b

f

outputs a value

a

to satisfy the following equation.

\newline

4a+7b=-52

\newline

Write a formula for

f(b)

b

\newline

f(b)=\square

Posted 6 months ago

Question

For a given input value

x

g

outputs a value

y

to satisfy the following equation.

\newline

-4x-6=-5y+2

\newline

Write a formula for

g(x)

x

\newline

g(x)=\square

Posted 10 months ago

Question

For a given input value

a

f

outputs a value

b

to satisfy the following equation.

\newline

-3a+6b=a+4b

\newline

Write a formula for

f(a)

a

\newline

f(a)=\square

Posted 10 months ago

Related topics

Algebra - Order of Operations Algebra - Distributive Property `X` and `Y` Axes Geometry - Scalene Triangle Common Multiple Geometry - Quadrant