Problem

Perform the indicated operations and write the result in standard form. \[ (-6-\sqrt{-5})^{2} \]

Solution

Step 1 :Given the complex number \((-6-\sqrt{-5})^{2}\)

Step 2 :We need to square this complex number. This involves squaring the real part, squaring the imaginary part, and then adding the two results together.

Step 3 :Let's denote the complex number as z. So, z = (-6-2.23606797749979i)

Step 4 :After squaring, we get the result as (31+26.832815729997478i)

Step 5 :This result is already in standard form, where the real part is 31 and the imaginary part is 26.832815729997478

Step 6 :So, the final answer in standard form is \(\boxed{31+26.83i}\)

From Solvely APP
Source: https://solvelyapp.com/problems/20772/

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