Complex Number Word Problems

Solutions

1 Calculate the value of k for the complex number obtained by dividing Complex Number Exercises. Note, it is represented in the bisector of the first quadrant.

2 Find the value of k for the quotient Complex Number Exercises, if it is:

1 A pure imaginary number.

2 A real number.

3 The complex number, 2 + 2 RAÍZ DE TRES is rotated 45° about the origin of its coordinates in an anti-clockwise direction. Find the complex number obtained after the turn.

4 Find the coordinates of the vertices of a regular hexagon of center origin, knowing that one of its vertices is the affix of complex number, 190°.

5Determine the value of b for the quotient Complex Number Exercises, if it equals: Complex Number Exercises

6What are the coordinates of the point that is obtained on having turned the affix of the complex 2 + i, 90° in an counterclockwise direction about the origin.

7 Find the coordinates of the vertices of a square of center origin, knowing that one vertex is the point (0, −2).

8 The sum of the real components of two conjugate complex numbers is six, and the sum of its modulus is 10. Determine these complex numbers.


Solved Complex Number Word Problems

1

Calculate the value of k for the complex number obtained by dividing Complex Number Exercises. Note, it is represented in the bisector of the first quadrant.

For the affix, (a, b), the complex number is on the bisector of the first quadrant. The following must be met: a = b.

Complex Number Operations

Complex Number Operations

Complex Number Operations

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Complex Number Solutions


2

Find the value of k for the quotient Complex Number Exercises, if it is:

1 A pure imaginary number.

Complex Number Operations

Complex Number Operations

Complex Number Operations

Complex Number Operations

Complex Number Solutions


2 A real number.

Complex Number Operations

Complex Number Solutions


3

The complex number, 2 + 2 RAÍZ DE TRES is rotated 45° about the origin of its coordinates in an anti-clockwise direction. Find the complex number obtained after the turn.

Complex Number Operations

Complex Number Solution


4

Find the coordinates of the vertices of a regular hexagon of center origin, knowing that one of its vertices is the affix of complex number, 190°.

The vertices are the affixes of the sixth roots of another complex number, z.

z = (190°)6 = 1540° = 1180°

Complex Number Operations

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Complex Number Operations

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Complex Number Solutions


5

Determine the value of b for the quotient Complex Number Exercises

Complex Number Operations

Complex Number Operations

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Complex Number Operations

Complex Number Solutions



6

What are the coordinates of the point that is obtained on having turned the affix of the complex 2 + i, 90° in an counterclockwise direction about the origin.

(2 + i) · 190° = (2 + i) · i = −1 + 2i = (−1,2)


7

Find the coordinates of the vertices of a square of center origin, knowing that one vertex is the point (0, −2).

(0, −2) = −2 i = 2 270

The vertices are the affixes of the quarter roots of another complex number, z.

Complex Number Operations

(2270°)4 = 161080º = 163 · 360° = 16

Complex Number Operations

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8

The sum of the real components of two conjugate complex numbers is six, and the sum of its modulus is 10. Determine these complex numbers.

z = a + bi = rα

z = a − bi = r−α

r + r = 10 flecha r = 5

a + a = 6 flecha a = 3

52 = 32 + b2        b=4

r cos α + r cos (−α) = 6

5 cos α + 5 cos α = 6

cos α = 3/5

α = 53° 7' 48''           α = 306° 52' 11''

3 + 4i = 553° 7' 48''

3 − 4i = 5306° 52' 11''