# Thread: Find Value of c

1. ## Find Value of c

The complex number
c + di is equal to (2 + i)^2. What is the value of c?

2. Originally Posted by magentarita
The complex number
c + di is equal to (2 + i)^2. What is the value of c?

So we have

$c+di = (2+i)^2$
first, me must expand the quantity $(2+i)^2$ so let's do that

$(2+i)^2 = (2+i)(2+i)$
$= 4+2i+2i+i^2$
$= 4+4i-1$
$= 3+4i$

So, we have

$c+di = 3+4i$
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.

3. ## ok...........

Originally Posted by caelum
So we have

$c+di = (2+i)^2$
first, me must expand the quantity $(2+i)^2$ so let's do that

$(2+i)^2 = (2+i)(2+i)$
$= 4+2i+2i+i^2$
$= 4+4i-1$
$= 3+4i$

So, we have

$c+di = 3+4i$
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.
A job well-done!