PRE CALCULUS Pre-Calculus Complex Numbers 2

Question 1

What is the modulus of the complex number 5 - 12i?

Accepted Answer

13

Answer

The modulus is √(5² + (-12)²) = √(25 + 144) = √169 = 13.

Question 2

Which of the following is equal to i⁵⁰?

Accepted Answer

-1

Answer

Since i repeats with period 4, i⁵⁰ = i^(4·12+2) = (i⁴)¹²·i² = 1·(-1) = -1.

Question 3

What is the argument (angle) of the complex number -1 + i in radians?

Accepted Answer

3π/4

Answer

The point (-1, 1) is in the second quadrant, so the argument is π - π/4 = 3π/4.

Question 4

If z = 3 + 4i, what is z · z̄ (z times its conjugate)?

Accepted Answer

25

Answer

z · z̄ = (3 + 4i)(3 - 4i) = 9 + 16 = 25 = |z|².

Question 5

Simplify: (2 + 3i)(2 - 3i)

Accepted Answer

13

Answer

(2 + 3i)(2 - 3i) = 4 - 9i² = 4 + 9 = 13.

PRE CALCULUS Practice Test