Simplify the expression (9 + 2i)(9 − 2i).

Question

26-11-2019
Mathematics

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Simplify the expression (9 + 2i)(9 − 2i).

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20savannahreedy 20savannahreedy · Answer 1 · 2019-11-26T18:11:15+01:00

Answer:

81 - 4i^2

Step-by-step explanation:

(9 + 2i)(9 - 2i)

Multiply First number in First parentheses to the first number in the second set of parentheses.

Multiply first number in the first parentheses with the second number in the second parentheses.

So you'll have:

81 - 18i

Then multiply the second number from the first parentheses by the first number in the second parentheses.

And multiply the second number in first parentheses by the second number in the second parentheses.

So then you'll have:

81 - 18i + 18i - 4i^2

Combine like terms:

81 - 4i^2

Final answer is:

81 - 4i^2

varshamittal029 varshamittal029 · Answer 2 · 2022-06-11T02:07:48+02:00

(9 + 2i)(9 − 2i)=85

What is the square of imaganiry number i?

The square of an imaginary number i is always -1. i.e. i²=-1

So according to asked question,

(9+2i)(9-2i)

using the algebric identity (a+b)(a-b)=a²-b²

where a=9 , b=2i

=(9)²-(2i)²

=9²-(4*i²)

=81-4i²

if we want to simplify the following expression

=81-(4(-1)) where i²=-1

=81+4

=85

Therefore (9 + 2i)(9 − 2i)=85

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