All categories

3 years ago

What is the product of 4+3i and 4-3i

2 answers:

8 0

So we know that i=the square root of -1 so
we multiply and notice that is is in the format of the differnece of two perfect squares which is (x)^2-(y)^2=(x-y)(x+y) so
we notice that 4=x and 3i=y so

(4-3i)(4+3i)=(4)^2-(3i)^2

(3 times the square root of -3)^2=(9 times -1)=-9
4^2 is 16
16-(-9)=subtracting a negative=adding a positive so =16+9=25
the answer is 25

mash [69]3 years ago

7 0

Use the formula $(a+b)(a-b)=a^2-b^2$ .

$(4+3i)(4-3i)=4^2-(3i)^2=16-9i^2 \\ \\
i^2=-1 \\ \\
16-9i^2=16-9 \times (-1)=16+9=25 \\ \\
\boxed{(4+3i)(4-3i)=25}$

You might be interested in

Debra plans to invest $2,250 for 10 years. She can invest in a savings account that pays 4% simple intrest or a savings account

Diano4ka-milaya [45]

Answer:

$\$180.55$

Step-by-step explanation:

step 1

Simple interest

we know that

The simple interest formula is equal to

$A=P(1+rt)$

where

A is the Final Investment Value

P is the Principal amount of money to be invested

r is the rate of interest

t is Number of Time Periods

in this problem we have

$t=10\ years\\ P=\$2,250\\r=4\%=4/100=0.04$

substitute in the formula above

$A=2,250(1+0.04*10)$

$A=2,250(1.4)$

$A=\$3,150$

step 2

Interest compounded annually

we know that

The compound interest formula is equal to

$A=P(1+\frac{r}{n})^{nt}$

where

A is the Final Investment Value

P is the Principal amount of money to be invested

r is the rate of interest in decimal

t is Number of Time Periods

n is the number of times interest is compounded per year

in this problem we have

$t=10\ years\\ P=\$2,250\\r=4\%=4/100=0.04\\n=1$

substitute in the formula above

$A=2,250(1+\frac{0.04}{1})^{1*10}$

$A=2,250(1.04)^{10}$

$A=\$3,330.55$

step 3

Find the differences between the two final amounts

$A=\$3,330.55-\$3,150=\$180.55$

5 0

3 years ago

The expression 60(0.75)^x represents the amount of a drug in milligrams that remains in the bloodstream after x hour. What was t

kogti [31]

It would be 60.

a(b)^x
Since a/ 60 would represent initial value.

7 0

3 years ago

Can anyone show me how to divide 931/7

Inessa [10]

(You go from left to right)
(Dividend is 931, divisor is 7)
Step 1: Look for a number smaller than 9 that is divisible by 7. 7 is the only one which is smaller than 9 and is divisible by 7. Now that you know 7*1=7, you put 1 above 931 (Dividend)
Step 2: You subtract that number from the number in tens place. And bring the leftover down.
Step 3: You repeat Step 1 and 2 until either you get a remainder of 0 or the remainder in smaller than the divisor (in this case 7)
(Therefore 931/7=133, quotient=133, remainder=0)
^Hope this helps.

7 0

3 years ago

Multiply 3.76 X.2 Show your work

WITCHER [35]

Answer:

7.52

Step-by-step explanation:

Write it out: 3.76 × 2
3.76 × 2 = 7.52

I hope this helps!

7 0

3 years ago

If a wall is in a 1/4 in scale drawing is 6 in tall how tall is the actual wall

vekshin1

So 1/4
that measn that the scale wall is 6 inches while the real wall is 4 times 6=24 inches tall (logically, it would be something like 1in/4ft so it woul dbe 24 feet not 24 inches but ok)

so 1/4
6 inches scale drawing is 1/4 of real wall
6=1/4 real
multiply by 4
24=real

asnwer is 24 inches

6 0

3 years ago