The problem asks to evaluate the expression $(-5 + \sqrt{-4}) + (3 - \sqrt{-16})$.

AlgebraComplex NumbersImaginary NumbersArithmetic Operations
2025/3/7

1. Problem Description

The problem asks to evaluate the expression (5+4)+(316)(-5 + \sqrt{-4}) + (3 - \sqrt{-16}).

2. Solution Steps

First, we simplify the square roots of negative numbers.
4=41=2i\sqrt{-4} = \sqrt{4} \cdot \sqrt{-1} = 2i
16=161=4i\sqrt{-16} = \sqrt{16} \cdot \sqrt{-1} = 4i
Now, substitute these values back into the original expression:
(5+2i)+(34i)(-5 + 2i) + (3 - 4i)
Next, we combine the real and imaginary parts separately:
(5+3)+(2i4i)(-5 + 3) + (2i - 4i)
22i-2 - 2i

3. Final Answer

22i-2 - 2i

Related problems in "Algebra"

The problem asks to solve the quadratic equation $2x^2 - 7x + 3 = 0$.

Quadratic EquationsFactoringQuadratic FormulaRoots of Equations
2025/7/16

The image shows an L-shaped figure. The dimensions of the outer rectangle are given as $(2x+5)$ mete...

AreaRectanglePolynomialsExpansion
2025/7/16

We are given three problems to solve. Problem 5: Find four consecutive numbers that sum to 22. Probl...

Linear EquationsConsecutive NumbersWord Problems
2025/7/16

We are presented with three separate math problems. Let's define $x$ as the unknown number for each ...

Linear EquationsWord ProblemsEquation Solving
2025/7/16

The problem is to find the determinant of the given matrix: $ \begin{bmatrix} 1 & 3 & 2 \\ 0 & 4 & 3...

Linear AlgebraMatricesDeterminants
2025/7/15

The problem consists of five questions: 1. Find the percentage error in measured length, calculated...

Percentage ErrorLinear EquationsExponentsLogarithmsArithmetic ProgressionStatisticsMeanVarianceCalculusDefinite IntegralConeGeometry
2025/7/15

The problem consists of three parts: (a) incomplete Table 2.2 for $y = 2x^2 - 4x - 3$, (b) drawing t...

Quadratic EquationsGraphsCalculus (Gradient)Functions
2025/7/15

We are given several math problems. We need to find the determinant and inverse of matrices, solve a...

MatricesDeterminantsInverse MatricesQuadratic EquationsCompleting the SquareMeanGeometryAreaVolumeTrigonometry
2025/7/15

The problem asks to multiply the expression $36x$ by $63y$.

Algebraic ExpressionsMultiplicationVariables
2025/7/15

We are asked to expand and simplify the expression $(y+3)(y-4)(2y-1)$. We are also asked to make $x$...

Polynomial ExpansionSimplificationFormula ManipulationSolving for a Variable
2025/7/15