Perform each operation. Write answers in standard form. (-8+2i)(-1+i)

Verified step by step guidance

1. Recall that to multiply two complex numbers, you use the distributive property (FOIL method): multiply each term in the first complex number by each term in the second complex number.
2. Write the expression explicitly: \((-8 + 2i)(-1 + i)\).
3. Multiply the terms: \((-8)(-1)\), \((-8)(i)\), \((2i)(-1)\), and \((2i)(i)\) separately.
4. Combine the results: \((-8)(-1) + (-8)(i) + (2i)(-1) + (2i)(i)\).
5. Simplify each term and remember that \(i^2 = -1\), then combine like terms (real parts together and imaginary parts together) to write the answer in standard form \(a + bi\).

Key Concepts

Complex Number Multiplication

Multiplying complex numbers involves using the distributive property (FOIL method) to expand the product of two binomials. Each term is multiplied, remembering that i² equals -1, which simplifies the expression.

Standard Form of a Complex Number

The standard form of a complex number is written as a + bi, where a is the real part and b is the imaginary coefficient. After multiplication, the result should be simplified and expressed in this form.

Properties of the Imaginary Unit i

The imaginary unit i is defined by i² = -1. This property is essential when simplifying expressions involving i, as it allows conversion of i² terms into real numbers, facilitating the simplification of complex number products.