Solve 1=a(2-(2+i))(2-(2-i))(2-3)(2-(-4))

$$1 = a ( 2 - ( 2 + i ) ) ( 2 - ( 2 - i ) ) ( 2 - 3 ) ( 2 - ( - 4 ) )$$

Solve for a

$$a=-\frac{1}{6}\approx -0.166666667$$

Steps for Solving Linear Equation

Subtract 2+i from 2 by subtracting corresponding real and imaginary parts.

$$1=a\left(2-2+i\right)\left(2-\left(2-i\right)\right)\left(2-3\right)\left(2-\left(-4\right)\right)$$

Subtract 2 from 2.

$$1=a\left(-i\right)\left(2-\left(2-i\right)\right)\left(2-3\right)\left(2-\left(-4\right)\right)$$

Subtract 2-i from 2 by subtracting corresponding real and imaginary parts.

$$1=a\left(-i\right)\left(2-2-i\right)\left(2-3\right)\left(2-\left(-4\right)\right)$$

Subtract 2 from 2.

$$1=a\left(-i\right)i\left(2-3\right)\left(2-\left(-4\right)\right)$$

Multiply -i and i to get 1.

$$1=a\left(2-3\right)\left(2-\left(-4\right)\right)$$

Subtract 3 from 2 to get -1.

$$1=a\left(-1\right)\left(2-\left(-4\right)\right)$$

The opposite of -4 is 4.

$$1=a\left(-1\right)\left(2+4\right)$$

Add 2 and 4 to get 6.

$$1=a\left(-1\right)\times 6$$

Multiply -1 and 6 to get -6.

$$1=a\left(-6\right)$$

Swap sides so that all variable terms are on the left hand side.

$$a\left(-6\right)=1$$

Divide both sides by -6.

$$a=\frac{1}{-6}$$

Fraction \frac{1}{-6} can be rewritten as -\frac{1}{6} by extracting the negative sign.

$$a=-\frac{1}{6}$$