If z is a complex number, then | 3z – 1 | = 3 | z – 2 | repr... | MATH - CONJUGATE, MODULUS AND ARGUMENT OF COMPLEX NUMBERS | SolveeIt | Solveeit

Today, August 18

Question

If z is a complex number, then | 3z – 1 | = 3 | z – 2 | represents

A

Y-axis

B

A circle

C

X-axis

D

A line parallel to y–axis

Answer

A line parallel to y–axis

Explanation

Solution

Sol. Let z = x + iy where x, yĪR

| 3z – 1 | = 3 | z – 2 |

| 3(x + iy) – 1| = 3 | x + iy – 2 |

9x² + 9y² – 6x + 1 = 9x² + 9y² – 36x + 36

30x = 35 Q x = $\frac{7}{6}$

A line parallel lie y-axis