First slide

Algebra of complex numbers

Question

$Let z \in C, if A = \{z : \arg (z) = \frac{π}{4}\} and B = \{z : \arg (z - 3 - 3 i) = \frac{2 π}{3}\} then$ $n (A \cap B) is equal to$

Moderate

A

1
B

2
C

3
D

0

Solution

$Arg (z) = \frac{π}{4}$
$\begin{array}{l} \Rightarrow T a n^{- 1} (\frac{y}{x}) = \frac{π}{4} \\ \Rightarrow y = x (x > 0, y > 0) \end{array}$
$\begin{array}{l} \arg (z - 3 - 3 i) = \frac{2 π}{\begin{array}{l} 3 \end{array}} \\ T a n^{- 1} (\frac{y - 3}{x - 3}) = 2 π / 3 \\ y - 3 = - \sqrt{3} (x - 3) (y - 3 > 0, x - 3 < 0) \end{array}$
We can observe that
$3 + 3 i \in A but \notin B$
$∴ n (A \cap B) = 0$

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App