Question

Find the multiplicative inverse
a. (2-5i)^2​

Answer 1

Answer:

z ( multiplicative inverse ) = 1/z = 1/-2+5i 1/-2+5i × -2-5i / -2-5i = -2-5i/(-2) square - (5i) = -2-5i / 4-(-25) [ because i(square)= -1] = -2-5i / 29 = -2/29 - 5i/29 Hence proved . ... The Questions and Answers of Find the reciprocal (or multiplicative inverse) of -2 + 5ia)b)c)d)Correct answer is option 'A'

Answer 2

Step-by-step explanation:

Given :-

(2-5i)^2

To find:-

Find the multiplicative inverse of (2-5i)^2

Solution:-

Given that : (2-5i)^2

This is in the form of (a-b)^2

Where , a = 2 and b = 5i

We know that

(a-b)^2 = a^2 - 2ab + b^2

=>(2-5i)^2

=>(2)^2 - 2(2)(5i) + (5i)^2

=>4-20i + 25i^2

We know that

i^2 = -1

=>4 -20i +25(-1)

=>4 - 20i -25

=>-20i-21

=>-(21+20i)

Multiplicative inverse of -(21+20i) is -1/(21+20i)

or

On Rationalising the denominator then

=>-1(21-20i)/(21+20i)(21-20i)

=>-(21-20i)/[(21)^2-(20i)^2]

=>-(21-20i)/(441-400i^2)

=>-(21-20i)/(441+400)

=>-(21-20i)/841

=>(-21+20i)/841

=>(20i-21)/841

Answer:-

The Multiplicative inverse of (2-5i)^2 is -1/(21+20i)

or (20i-21)/841

Used Concept:-

• The product of any two numbers is 1 then the both numbers are called Multiplicative inverse of each other.