Z^5=-243i, find the solution to the equation whose argument is strictly between 180 degrees and 270 degrees. Round your answer to the nearest 10th

The solution is .

Step-by-step explanation:

Complex power is determined by means of the De Moivre's Theorem, whose expression is:

Where is the norm of the complex number. In this case, expression can be written as:

The real component must be equal to zero and complex component must be equal to -1. That is to say:

Possible solutions for each component are, respectively:

Real component

,

,

Possible solutions: , ,

Complex component

,

,

Possible solutions: ,

There is one solution whose argument is strictly between 180 degrees () and 270 degrees ().

answer: i think it is (1,-2)

x =-.20752

step-by-step explanation:

4^(x+2)=12

4^(x+2)=12

take the log base 4 on each side

log 4 (4^(x+2) = log 4(12)

we know log b(a^y) = y log b (a)

(x+2) log 4(4) = log 4 (12)

x+2 = log 4 (12)

we know   logb c = loga c/loga b

we want to convert to base 10   so a = 10

by default, we do not write the 10   c = 4   and b = 10

log4 10 = log 12/log 4

log4 10 = log 12/ log 4

x+2 = log 12/ log 4

subtract 2 from each side

x +2 -2 = log 12/ log 4 -2

x = 1.79248125 -2

x =-.20752