Question

evaluate the subtraction (13 + \sqrt{-225}) - (\sqrt{49} - 2i). provide the answer in the form of a + bi (1 point)

Explanation:

Step1: Simplify square roots of negative numbers

Recall that \(\sqrt{-n}=\sqrt{n}\cdot i\) for positive real numbers \(n\). So, \(\sqrt{-225}=\sqrt{225}\cdot i = 15i\) and \(\sqrt{49}=7\). Substitute these into the expression: \((13 + 15i)-(7 - 2i)\).

Step2: Distribute the negative sign

Distribute the subtraction sign to both terms inside the second parentheses: \(13 + 15i - 7 + 2i\).

Step3: Combine like terms

Combine the real parts (\(13 - 7\)) and the imaginary parts (\(15i + 2i\)): \((13 - 7)+(15i + 2i)=6 + 17i\).

Answer:

\(6 + 17i\)