# Work each problem. Show that -2-i is a solution of the equation x^{2}+4x+5=0

Work each problem. Show that -2-i is a solution of the equation ${x}^{2}+4x+5=0$
You can still ask an expert for help

• Questions are typically answered in as fast as 30 minutes

Solve your problem for the price of one coffee

• Math expert for every subject
• Pay only if we can solve it

oppturf

Prove that the given complex number is a solution of the equation.
$$\displaystyle{x}^{{{2}}}+{4}{x}+{5}={0}$$ Write the equation
$$(-2-i)^{2}+4(-2-i)+5=0$$Substitute « with the complex number
$$4+4i+i^{2}+4(-2-i)+5=-0$$Use square of binomial
$$4+4i+i^{2}-8-4i+5=0$$ Use distributive property
$$4+4i+(-1)-8-4i+5=0$$ Evaluate the exponent
(4-1-8+5)+(4—4)i Separate real parts and imaginary parts
0+0i=0 Simplify
0=0 Statement is true