NCERT Class 11-Math's: Chapter –5 Complex Numbers and Quadratic Equations Part 10

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Question 16:

are two complex numbers such that and then show that .

Answer:

Let

Given that

And

Now,

Hence proved.

Question 17:

If then show that the real part of is zero.

Answer:

Let

Now,

Since

Hence, the real part of is zero.

Question 18:

If are two pairs of conjugate complex numbers, then find

Answer:

Given and are conjugate complex numbers.

is,

He negative side of the real axis

Similarly,

Question 19:

If , then

Show that

Answer:

Given

Now,

Hence Proved.