To find the value of m and n set the real parts equal to each other and the imaginary parts equal to each other and then solve the two equations.
\Real parts:
\Imaginary parts:
\Solve the equations by substitution method.
\Consider the equation
Apply subtraction property of equality: if a = b, then.
(Subtract 2n from each side)
(Apply additive inverse property:
)
Substitute in equation
Distribute terms using distributive property: .
(Multiply:
)
(Subtract:
)
(Subtract 10 from each side)
Apply commutative property of addition: a + b = b + a.
\ (Apply additive inverse property:
)
(Subtract:
)
Apply division property of equality: if a = b, then.
(Divide each side by negative 5)
(Cancel common terms)
Substitute in equation
.
(Multiply:
)
(Subtract:
)
The solutions is (3, 1).