The complex numberc + di is equal to (2 + i)^2. What is the value of c?
So we have
$\displaystyle c+di = (2+i)^2$
first, me must expand the quantity $\displaystyle (2+i)^2$ so let's do that
$\displaystyle (2+i)^2 = (2+i)(2+i)$
$\displaystyle = 4+2i+2i+i^2$
$\displaystyle = 4+4i-1$
$\displaystyle = 3+4i$
So, we have
$\displaystyle c+di = 3+4i$
In complex numbers the real part must equate with the real part and the imaginary part must equate with the imaginary part in a complex number so c must equal 3 since it is the only real part of 3+4i.