if (2+2i)squared= a+bi, compute the value of a+b.
To compute the value of a+b, we need to first square the complex number (2+2i). Let's break down the process step by step:
Step 1: Start with the complex number (2+2i) and square it.
(2+2i)^2
Step 2: Use the equation (a + bi)^2 = (a^2 - b^2) + 2abi to simplify.
(a^2 - b^2) + 2abi
Step 3: Substitute the given values of a and b with the real and imaginary parts of (2+2i).
(a^2 - b^2) + 2abi = (2^2 - 2^2) + 2(2)(2i)
= (4 - 4) + 4i
= 0 + 4i
So, the value of a is 0 and the value of b is 4. Therefore, a+b = 0+4 = 4.