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N-CN.2 Warmup M2-056-A10-V01

Add, subtract, and multiply complex numbers using i^2=-1 and algebraic properties.

Add complex numbers geometrically on the complex plane by combining real and imaginary coordinates

Problem

Add \((2+3i)+(4+i)\) component-wise, then map the sum \(a+\text{bi}\) to the complex-plane point \((a,b)\).

Prompt complex plane with addend vectors 2 + 3i, represented by (2, 3), and 4 + i, represented by (4, 1), each drawn from the origin. The head-to-tail resultant and sum point are withheld. Open full size
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What this problem is really about

Geometric complex addition is vector addition of real and imaginary coordinates. We’ll map each number to a horizontal-vertical pair, add corresponding components, locate the resultant endpoint, translate it back to standard form, and verify with algebraic addition.

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Four variants of this problem type
Curriculum context
Course
Math II
Standard
N-CN.2
Category
Number and Quantity
Domain
The Complex Number System
Objective
Add, subtract, and multiply complex numbers using i^2=-1 and algebraic properties.
Problem type
Add complex numbers geometrically on the complex plane by combining real and imaginary coordinates