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Basic Arithmetic with Complex Numbers

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Suppose \( z = 5 + 3i \) and \( w = 2 - 4i \). Find: (a) \( z+w \), (b) \( z- w \), (c) \( zw \). Use the ordinary rules of algebra together with \( i^2 = -1 \) to obtain a result in the standard form \( a + bi \).
complex-numberscomplex-arithmeticadditionsubtractionmultiplicationreal-partimaginary-partimaginary-unitalgebraic-expansionstandard-form

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What this problem tests

Tests the ability to apply standard algebraic rules to complex numbers, including distributing negative signs, expanding binomials, and simplifying using \( i^2 = -1 \).

This is a foundational exercise in complex arithmetic, typically encountered at the beginning of a linear algebra or precalculus course before studying vector spaces over the complex field.

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