Simplify the complex number (13+14i)^2

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justaguide's profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

We have to simplify (13+14i)^2.

(13+14i)^2

=> (13+14i)*(13+14i)

multiply all the terms

=> 13*13 + 13*14i + 13*14i + 14i*14i

=> 169 + 364i + 196*i^2

As i^2 = 1

=> 169 - 196 + 364i

=> -27 + 364i

Therefore (13+14i)^2 = -27 + 364i

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neela | High School Teacher | (Level 3) Valedictorian

Posted on

To simplify the complex number (13+14i)^2.

(13+14i)^2 = (13+14i)13+14)i)

(13+14i)^2 = 13(13+14i) + 14i(13+14i).

(13+14i)^2 =13*13 + 13*14i + 14i*13+14i*14i

(13+14i)^2 = 169 + (182+182)i +196i^2

(13+14i)^2 = 169 +364i -196.

(13+14i)^2 = 169-196 + 364i.

(13+14i)^2 = -27+364i

giorgiana1976's profile pic

giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

To simplify the complex number raised to square, we'll expand the square, using the formula:

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

We'll put a = 13 and b = 14i:

(13 + 14i)^2 = 13^2 + 2*13*14i + (14i)^2

(13 + 14i)^2 = 169 + 364i + 196i^2

Since i^2 = -1, we'll get:

(13 + 14i)^2 = 169 + 364i - 196

We'll combine the real parts:

(13 + 14i)^2 = -27 + 364i

The simplified form of the complex number raised to square is:

(z)^2 = -27 + 364i, where z = 13 + 14i

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