question\nsimplify the expression to ( a + bi ) form:\n( sqrt{4}-sqrt{-81}+sqrt{4}+sqrt{-36} )
question\nsimplify the expression to ( a + bi ) form:\n( sqrt{4}-sqrt{-81}+sqrt{4}+sqrt{-36} )
Answer
Explanation:
Step1: Simplify square roots
$$ \begin{align*} \sqrt{4}& = 2\ \sqrt{-81}&=\sqrt{81\times(- 1)} = 9i\ \sqrt{4}& = 2\ \sqrt{-36}&=\sqrt{36\times(-1)}=6i \end{align*} $$
Step2: Substitute into the expression
Substitute the simplified values into the original expression (\sqrt{4}-\sqrt{-81}+\sqrt{4}+\sqrt{-36}), we get (2 - 9i+2 + 6i)
Step3: Combine like - terms
Combine the real parts (2 + 2=4) and the imaginary parts (-9i+6i=-3i)
Answer:
(4-3i)