Simplify (4+3i)^2.

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justaguide's profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

We have to simplify (4+3i)^2.

Now, let's open the brackets.

(4+3i)^2

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

=> 16 + 9*i^2 + 24i

=> 16 - 9 + 24i

=> 7 + 24i

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

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 = 4 and b = 3i:

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

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

But i^2 = -1

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

We'll combine the real parts:

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

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

(z)^2 = 7 + 24i, where z = 4+3i.

neela's profile pic

neela | High School Teacher | (Level 3) Valedictorian

Posted on

To simplify (4+3i)^2.

We simplify the above and bring the result  as x+yi form.

(4+3i)^2 = 4^2+4*3i+(3i)^2, as (a+b)^2 = a^2+2ab+b^2.

(4+3i)^2 = 16 + 12i +9i^2.

(4+3i)^2 = 16+12i -9, as i^2 = -1.

(4+3i)^2 = = 16-9 +12i 

(4+3i)^2 = 7+12i is the form of x+yi.

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