Exercises: Add, Subtract, and Multiply Complex Numbers

Show your work. Write all answers in standard form $a + bi$ .

Grade 9·21 problems·~30 min·Common Core Math - HS Number and Quantity·standard·hsn-cn-a-2

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Warm-Up: Review What You Know

Combine like terms: $(3x + 2) + (5x - 1)$ .

$8x + 1$

$8x + 3$

$8x - 1$

$8x + 2$

What is the value of $i^2$ ?

$1$

$-i$

$-1$

$i$

Expand $(2 + 3)(2 - 3)$ using the difference-of-squares pattern $(a + b)(a - b) = a^2 - b^2$ .

$4 + 9 = 13$

$4 - 9 = -5$

$4 - 6 = -2$

$4 + 6 = 10$

Compute $(3 + 2i) + (5 - i)$ . Write the real part only. Enter a number.

Compute $(4 + 3i) - (1 + 5i)$ . Write the imaginary part (the coefficient of $i$ ). Enter a number.

Compute $(2 + 3i)(1 - 4i)$ .

$2 - 12i^2$

$2 - 5i - 12i^2$ (not yet simplified)

$14 - 5i$

$-10 - 5i$

Compute $(1 + 2i)^2$ .

$1 + 4i^2 = 1 - 4 = -3$

$5$

$-3 + 4i$

$1 + 4$

Compute $(3 + 4i)(3 - 4i)$ . Enter the numerical result (it will be a real number).

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