Answer:
We want to solve the equation:
(6 - 1) + (3m)i = -12 + 27i
Where m is a complex number.
first, we can rewrite this as:
5 + 3*m*i = -12 + 27*i
3*m*i = -12 - 5 + 27*i
3*m*i = -17 + 27*i
And we can write m as:
m = a + b*i
Replacing that in the above equation we get:
3*(a + b*i)*i = -17 + 27*i
3*a*i + 3*b*i^2 = -17 + 27*i
and we know that i^2 = -1
3*a*i - 3*b = -17 + 27*i
The real part in the left (-3*b) must be equal to the real part in the right (-17)
then:
-3*b = -17
b = -17/-3 = 17/3
And the imaginary part in the left (3*a) must be equal to the imaginary part in the right (27)
then:
3*a = 27
a = 27/3.
Then the value of m is:
m = a + b*i = (27/3) + (17/3)*i
