NCERT Class 11-Math's: Chapter –5 Complex Numbers and Quadratic Equations Part 3
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Question 2:
If where show that
Answer:
i.e.,
Thus
So, .
Question 3:
Solve the equation where
Answer:
From (2), we have
When from(1), we get i.e., .
When from(1), we get
Hence, the solutions of the given equation are
Question 4:
If the imaginary part of is , then show that the locus of the point representing in the Argand plane is a straight line.
Answer:
Let Then
Thus
But
So
, which is the equation of a line.
Question 5:
If , then show that z lies on imaginary axis.
Answer:
Let Then
Hence z lies on
Question 6:
Let and be two complex numbers such that and Then find
Answer:
Given that
Thus
Question 7:
Let and be two complex numbers such that .
Then show that .
Answer:
Let and
Where .
We have,