NCERT Class 11-Math's: Chapter –5 Complex Numbers and Quadratic Equations Part 12

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Question 24:

If and are two complex numbers such that , then show that .

Answer:

Let

Given

Also

Now,

get

to zero, we get

Hence proved.

Objective Type Questions

Question 25:

Fill in the blanks of the following

(i) For any two complex numbers and any real numbers a, b, __________

(ii) The value of is__________.

(iii) The number is equal to _________.

(iv) The sum of the series Upto term is ________

(v) Multiplicative inverse of is _____________

(vi) If and are complex numbers such that is a real number, then _____

(vii) is ____________

(viii) If , then the greatest and least values of are _________and_______

(ix) If , then the locus of is _________

(x) If then ________

Answer:

(i)

(ii)

(iii)

(iv)

(v)

(vi)

(vii)

(viii)

(ix) a circle

(x)

Question 26:

State True or False for the following:

(i) The order relation is defined on the set of complex numbers.

(ii) Multiplication of a non-zero complex number by – i rotates the point about origin through a right angle in the anti-clockwise direction.

(iii) For any complex number z the minimum value of .

(iv) The locus represented by is a line perpendicular to the join of

(v) If is a complex number such that and , then .

(vi) The inequality represents the region given by .

(vii) Let be two complex numbers such that then

(viii) 2 is not a complex number

Answer:

(i) F

(ii) F

(iii) T

(iv) T

(v) T

(vi) T

(vii) F

(viii) F