Complex Numbers Adding & Subtracting

When adding and subtracting complex numbers you combine the like terms. The real terms get combined and the imaginary terms (containing $i$ ) get combined.

$(a + b i) + (c + d i) = (a + c) + (b + d) i$

$(a + b i) - (c + d i) = (a - c) + (b - d) i$

Practice Problems

$1)$ Simplify $(6 + 4 i) + (3 - 2 i)$
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The answer is $9 + 2 i$

$2)$ Simplify $(5 - 3 i) - (3 + 2 i)$
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The answer is $2 - 5 i$

$3)$ Simplify $(7 - 5 i) + (7 - 3 i)$

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The answer is $14 - 8 i$

$4)$ Simplify $(2 + i) - (3 - 2 i)$

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The answer is $- 1 + 3 i$

$5)$ Simplify $(15 + 6 i) + (5 - 6 i)$

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The answer is $20$

$6)$ Simplify $(8 + 3 i) - (8 - 3 i)$

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The answer is $6 i$

$7)$ Simplify $(2 + 5 i) + (2 + 5 i)$

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The answer is $4 + 10 i$

$8)$ Simplify $(3 + 6 i) + (- 5 + 2 i)$

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The answer is $- 2 + 8 i$

$9)$ Simplify $(1 + i) + (3 + 4 i)$

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The answer is $4 + 5 i$

$10)$ Simplify $(2 + 3 i) - (3 + 6 i)$

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The answer is $- 1 - 3 i$

$11)$ Simplify $(4 - 2 i) + (3 - 4 i)$

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The answer is $7 - 6 i$

$12)$ Simplify $(- 2 + 5 i) + (1 - 3 i)$

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The answer is $- 1 + 2 i$

$13)$ Simplify $(- 3 + 2 i) - (4 - 2 i)$

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The answer is $- 7 + 4 i$

$14)$ Simplify $(6 + 7 i) - (2 - 3 i)$

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The answer is $4 + 10 i$

$15)$ Simplify $(1 + 2 i) + (2 - 5 i)$

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The answer is $3 - 3 i$

$16)$ Simplify $(5 - 6 i) - (3 + 2 i)$

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The answer is $2 - 8 i$

$17)$ Simplify $(4 + 3 i) - (5 + 4 i)$

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The answer is $- 1 - i$

$18)$ Simplify $(2 + 5 i) + (3 - 6 i)$

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The answer is $5 - i$

$19)$ Simplify $(5 - 2 i) - (2 + 3 i)$

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The answer is $3 - 5 i$

$20)$ Simplify $(3 + 4 i) - (4 - 2 i)$

Show Answer
The answer is $- 1 + 6 i$

See Related Pages

$∙ Complex Numbers Calculator (Symbolab.com)$

$∙ Adding and Subtracting Polynomials$
$(4 d + 7) - (2 d - 5) \dots$

$∙ Multiplying Polynomials$
$(x + 2) (x^{2} + 3 x - 5) \dots$

$∙ Dividing Polynomials$
$(x^{3} - 8) \div (x - 2) \dots$

$∙ Dividing Polynomials (Synthetic Division)$
$(x^{3} - 8) \div (x - 2) \dots$

$∙ Synthetic Substitution$
$f (x) = 4 x^{4} - 3 x^{2} + 8 x - 2 \dots$

$∙ End Behavior$
$As x \to \infty, f (x) \to \infty$
$As x \to - \infty, f (x) \to \infty \dots$

$∙ Completing the Square$
$x^{2} + 10 x - 24 = 0 \dots$

$∙ Quadratic Formula and the Discriminant$
$x = - b \pm \frac{\sqrt{b^{2} - 4 a c}}{2 a} \dots$

$∙ Multiplicity of Roots$
$\dots$

$∙ Rational Zero Theorem$
$\pm 1, \pm 2, \pm 3, \pm 4, \pm 6, \pm 12 \dots$

$∙ Descartes Rule of Signs$

$∙ Roots and Zeroes$
$Solve for x . 3 x^{2} + 4 x = 0 \dots$

$∙ Linear Factored Form$
$f (x) = (x + 4) (x + 1) (x - 3) \dots$

$∙ Polynomial Inequalities$
$x^{3} - 4 x^{2} - 4 x + 16 > 0 \dots$

$∙ Andymath Homepage$

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