Answer: a) √50
b) n = 1 + 7i
Step-by-step explanation:
first, the modulus of a complex number z = a + bi is
IzI = √(a^2 + b^2)
The fact that n is complex does not mean that n doesn't has a real part, so we must write our numbers as:
m = 2 + 6i
n = a + bi
Im + nI = 3√10
Im + n I = √(a^2 + b^2 + 2^2 + 6^2)= 3√10
= √(a^2 + b^2 + 40) = 3√10
a^2 + b^2 + 40 = 3^2*10 = 9*10 = 90
a^2 + b^2 = 90 - 40 = 50
√(a^2 + b^2 ) = InI = √50
The modulus of n must be equal to the square root of 50.
now we can find any values a and b such a^2 + b^2 = 50.
for example, a = 1 and b = 7
1^2 + 7^2 = 1 + 49 = 50
Then a possible value for n is:
n = 1 + 7i
Answer:
he must have 200000 dollars to earn 6000 in commission
Answer:
41
Step-by-step explanation:
each page holds 7 discs. the alb holds 700 discs. that means there are 100 pages. 69% of the pages are empty so therefore 41 pages are filled.
Answer:
They are supplementary
Step-by-step explanation:
Since AB and DC are parallel, then the alternate interior angles are congruent because there is transversal cutting the parallel lines (BC). So m<B is supplementary to m<C
Answer:
1:
we have a rule that is (n-2)×180
while n = number of sides
2:
exterior angle of a polygon = 360 ÷ number of sides
so 360÷25=14.4
3:
octagon is 8 side, so as we said: (8-2)×180 = 1080
4:
lets make an equation, we know that (n-2)×180 = the sum
so (x-2)×180=720
180x -360 = 720
180x = 1080
x=6
