Answer:
251.2 cm
Step-by-step explanation:
It just is
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
The simple answer (not using multiples of 2
(360°)) is
![= \sqrt[3]{125} ((cos( \frac{288}{3})) + isin(( \frac{288}{3}))) = 5(cos96 + isin96)](https://tex.z-dn.net/?f=%3D%20%20%5Csqrt%5B3%5D%7B125%7D%20%28%28cos%28%20%5Cfrac%7B288%7D%7B3%7D%29%29%20%2B%20isin%28%28%20%5Cfrac%7B288%7D%7B3%7D%29%29%29%0A%3D%20%205%28cos96%20%2B%20isin96%29)
