PRE CALCULUS Pre-Calculus Complex Numbers 4

Question 1

Solve for x: x² + 25 = 0

Accepted Answer

x = ±5i

Answer

x² = -25, so x = ±√(-25) = ±5i.

Question 2

What is the sum of a complex number and its conjugate?

Accepted Answer

2a

Answer

(a + bi) + (a - bi) = 2a, which is always a real number.

Question 3

In the complex plane, which direction does multiplying by i rotate a vector?

Accepted Answer

90° counterclockwise

Answer

Multiplying by i = cos90° + i sin90° rotates a vector 90° counterclockwise.

Question 4

What is i²⁰²⁶?

Accepted Answer

-1

Answer

2026 mod 4 = 2 (since 4 × 506 = 2024), so i²⁰²⁶ = i² = -1.

Question 5

The cube roots of unity are the solutions to which equation?

Accepted Answer

z³ = 1

Answer

The cube roots of unity satisfy z³ = 1 and are equally spaced at 120° apart on the unit circle.

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