Solve (m-1)^2+(m+i)^2

$$( m - 1 ) ^ { 2 } + ( m + i ) ^ { 2 }$$

Evaluate

$$2m\left(m+\left(-1+i\right)\right)$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(m-1\right)^{2}.

$$m^{2}-2m+1+\left(m+i\right)^{2}$$

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(m+i\right)^{2}.

$$m^{2}-2m+1+m^{2}+2im-1$$

Combine m^{2} and m^{2} to get 2m^{2}.

$$2m^{2}-2m+1+2im-1$$

Combine -2m and 2im to get \left(-2+2i\right)m.

$$2m^{2}+\left(-2+2i\right)m+1-1$$

Subtract 1 from 1 to get 0.

$$2m^{2}+\left(-2+2i\right)m$$

Expand

$$2m^{2}+\left(-2+2i\right)m$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(m-1\right)^{2}.

$$m^{2}-2m+1+\left(m+i\right)^{2}$$

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(m+i\right)^{2}.

$$m^{2}-2m+1+m^{2}+2im-1$$

Combine m^{2} and m^{2} to get 2m^{2}.

$$2m^{2}-2m+1+2im-1$$

Combine -2m and 2im to get \left(-2+2i\right)m.

$$2m^{2}+\left(-2+2i\right)m+1-1$$

Subtract 1 from 1 to get 0.

$$2m^{2}+\left(-2+2i\right)m$$