Squared complex numbers.Square (4+3i)^2.

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justaguide's profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

We have to find the square of (4+3i)

(4+3i)^2

=> (4+3i)(4+3i)

=> 4*4 + 4*3*i + 4*3*i + 3*i*3*i

=> 16 + 12i + 12i + 9i^2

i^2 = -1

=> 16 + 24i - 9

=> 7 + 24i

The required square is 7 + 24i

giorgiana1976's profile pic

giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

To square the complex number, we'll apply the formula:

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

We'll put a = 4 and b = 3i and we'll expand the binomial:

(4+3i)^2 = 4^2 + 2*4*3i + (3i)^2

(4+3i)^2 = 16 + 24i + 9i^2

We'll replace i^2 by -1:

(4+3i)^2 = 16 + 24i - 9

We'll combine the real parts:

(4+3i)^2 = 7 + 24i

The complex number raised to square is: (4+3i)^2 = 7 + 24i.

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