c + di is equal to (2 + i)^2?

Answer 1

I guess you're just supposed to write out (2 + i)^2.

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

Answer 2

If you wish to solve for 'c' and 'd', we have:

c + di = (2 + i)^2

= (2 + i)(2 + i) = 4 + 4i + i^2

= 4 + 4i - 1 = 3 + 4i.

Equating real and imaginary parts on the two sides:

c = 3 and d = 4.

Answer 3

(2 + i)² =
2² + 2•2i + i² =
4 + 4i - 1 =
3 + 4i

so c = 3, d = 4

Answer 4

c + di = (2 + i)^2
c + di = 2^2 + 2*2*i + i^2
c + di = 4 + 4i - 1
c + di = 3 + 4i

The numbers on left side and right side are both complex.
Two complex numbers are equal only if their real and imaginary parts are separately equal.

Here, for (c + di) real part = c and imaginary part = d
and for (3 + 4i) real part = 3 and imaginary part = 4

So c = 3, d = 4

Answer 5

(2 + i).(2 + i) = 4 + 4i - 1 = 3 + 4i
c = 3
d = 4