What is the answer to (2+i)^2=c+di ?

The answer to (2+i)^2=c+di is c=3,d=4

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(2+i)^2=c+di

(2 + i)^{2} = c + d i

c = 3, d = 4

Solution steps

(2 + i)^{2} = c + d i

Expand

(2 + i)^{2} : 3 + 4 i

3 + 4 i = c + d i

Complex numbers can be equal only if their real and imaginary parts are equalRewrite as system of equations:

[3 = c 4 = d]

[3 = c 4 = d] : c = 3, d = 4

c = 3, d = 4

(z) \cdot z = 4 + 6 i

z^{2} + 2 (1 + i) z + 3 - 2 i = 0

x + y i = \frac{1}{i}, x, x + y

x^{2} = 2 + 23 i

z^{2} = 9 i