Answer
$a = - \frac{29}{5}$
$b = \frac{11}{5}$
Work Step by Step
$2ia+(5+3i)b = 11-5i$
Expand the above expression:
$2ia + 5b + 3ib = 11-5i$
Combine like terms:
$(5b) + (2a+3b)i = 11 - 5i$
In order for the complex number to equal $11-5i$, the real component must equal $11$ and the imaginary component must equal $-5$.
Equation 1: This is an expression from the real component of the complex number.
$5b = 11$
Equation 2: This is an expression from the imaginary component of the complex number.
$2a + 3b = -5$
Solve the above system of equations using substitution:
Solve Equation 1 to determine the value of b:
$b = \frac{11}{5}$
Substitute the value of b into Equation 2 to solve for the value of a:
$2a + 3(\frac{11}{5}) = -5$
$2a + \frac{33}{5} = -5$
$2a = -5 - \frac{33}{5}$
$2a = - \frac{58}{5}$
$a = - \frac{29}{5}$
In summary:
$a = - \frac{29}{5}$
$b = \frac{11}{5}$
