Question

Let the equation of a straight line $L$ in complex form be $a\bar{z}+\bar{a}z+b=0$, where a is a complex number and $b$ is a real number, then

• A. the straight line $\frac{z-c}{a}+\frac{i(\bar{z}-\bar{c})}{\bar{a}}=0$ makes an angle of $45^{\circ }$ with $L$ and passes through a point $c$ (where $c$ is a complex number)
• B. the straight line $\frac{z-c}{a}=\frac{i(\bar{z}-\bar{c})}{\bar{a}}$ makes an angle of $45^{\circ }$ with $L$ and passes through a point $c$ (where $c$ is a complex number)
• C. the complex slope of the line $L$ is $-\frac{a}{\vec{a}}$.
• D. the complex slope of the line $L$ is $\frac{a}{\bar{a}}$.

Answer 1

Answer: (A), (B), (C)

Correct answer is (a) the straight line $\frac{z-c}{a}+\frac{i(\bar{z}-\bar{c})}{\bar{a}}=0$ makes an angle of $45^{\circ }$ with $L$ and passes through a point $c$ (where $c$ is a complex number) Correct answer is (b) the straight line $\frac{z-c}{a}=\frac{i(\bar{z}-\bar{c})}{\bar{a}}$ makes an angle of $45^{\circ }$ with $L$ and passes through a point $c$ (where $c$ is a complex number) Correct answer is (c) the complex slope of the line $L$ is $-\frac{a}{\vec{a}}$.