Let z1 and z2 be two complex numbers such that
\(z_1=iz_2 \,and \,arg(\frac{z_1}{z_2})=π.\)
Let z1 and z2 be two complex numbers such that
\(z_1=iz_2 \,and \,arg(\frac{z_1}{z_2})=π.\)
- \(arg \,z_2=(\frac{\pi}{4})\)
- \(arg \,z_2=-(\frac{3\pi}{4})\)
- \(arg \,z_1=(\frac{\pi}{4})\)
- \(arg \,z_1=-(\frac{3\pi}{4})\)
The Correct Option is A
Solution and Explanation
The correct option is: (C).
∵\(\frac{z_1}{z_2}=i⇒z_1=-iz_2\)
\(⇒arg(z_1)=-\frac{\pi}{2}+arg(z_2).....(i)\)
Also
arg(z1)-arg(z2)= π
⇒ arg(z1) + arg(z2) = π …(ii)
From (i) and (ii), we get
\(arg(z_1)=\frac{\pi}{4} and\,arg(z_2)=\frac{3\pi}{4}\)
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Concepts Used:
Complex Number
A Complex Number is written in the form
a + ib
where,
- “a” is a real number
- “b” is an imaginary number
The Complex Number consists of a symbol “i” which satisfies the condition i^2 = −1. Complex Numbers are mentioned as the extension of one-dimensional number lines. In a complex plane, a Complex Number indicated as a + bi is usually represented in the form of the point (a, b). We have to pay attention that a Complex Number with absolutely no real part, such as – i, -5i, etc, is called purely imaginary. Also, a Complex Number with perfectly no imaginary part is known as a real number.