Question

How do you simplify ${\left( {1 + i} \right)^2}$ ?

Answer 1

Hint:For simplifying this we will use the formula ${\left( {a + b} \right)^2} = {a^2} + {b^2} + 2ab$ and by using this and expanding it we will be able to solve this question. And also we know the value of ${i^2} = - 1$ . So we will put this and solve it to get the simplification of the above question.

Formula used:
The algebraic formula is given by,
${\left( {a - b} \right)^2} = {a^2} + {b^2} - 2ab$

Complete step by step answer:
So an equation is given as ${\left( {1 + i} \right)^2}$ . So to simplify this equation we will first expand the equation by using the formula ${\left( {a - b} \right)^2} = {a^2} + {b^2} - 2ab$ . So on expanding we will get the equation as
$ \Rightarrow {1^2} + 2 \cdot 1 \cdot i + {i^2}$
As we know the value of ${i^2}$ will always equal one. Therefore, on substituting the values, we will get the equation as
$ \Rightarrow 1 + 2i - 1$
And on solving the addition and subtraction in the above equation, we will get the equationas
$ \Rightarrow 2i$

Therefore, on simplifying ${\left( {1 + i} \right)^2}$ , we will get $2i$.

Note: For simplifying this type of question we just need to keep an eye on the question and we have to think about how we can change this question and can use the formula to solve it. So this will come with practice. So practicing such questions is necessary. Also, we need to remember the value of iota.