Question

Express the following in the form of a+ib, where a,b=R
i=√-1. State the values of a and b. ​

Answer 1

Answer:  The required answer is $E=14-\sqrt5+i,$ where a = 14 - √5  and  b = 1.

Step-by-step explanation:  We are given to express the following expression in the form of a + ib, where a, b are reals and  i=√-1 :

$E=(-\sqrt5+2\sqrt{-4})+(1-\sqrt{-9})+(2+3i)(2-3i).$

We will be using the following formula :

$(x+y)(x-y)=x^2-y^2.$

So, we have

$E\\\\=(-\sqrt5+2\sqrt{-4})+(1-\sqrt{-9})+(2+3i)(2-3i)\\\\=(-\sqrt5+2\times 2i)+(1-3i)+2^2-(3i)^2\\\\=-\sqrt5+4i+1-3i+4-9i^2\\\\=5-\sqrt5+i+9\\\\=14-\sqrt5+i.$

Thus, the required answer is $E=14-\sqrt5+i,$ where a = 14 - √5  and  b = 1.