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

Bergen 2021-09-24 Answered
Work each problem. Show that -2-i is a solution of the equation x2+4x+5=0
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Expert Answer

oppturf
Answered 2021-09-25 Author has 94 answers

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

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