What is the answer to (a+bi)^2=(a+b)(a-b)+2abi ?

The answer to (a+bi)^2=(a+b)(a-b)+2abi is No Solution

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(a+bi)^2=(a+b)(a-b)+2abi

(a + bi)^{2} = (a + b) (a - b) + 2 abi

No Solution

Solution steps

(a + bi)^{2} = (a + b) (a - b) + 2 abi

Expand

(a^{2} - b^{2}) + 2 iab = (a^{2} - b^{2}) + 2 iab

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

[a^{2} - b^{2} = a^{2} - b^{2} 2 ab = 2 ab]

[a^{2} - b^{2} = a^{2} - b^{2} 2 ab = 2 ab] : No Solution

No Solution

z^{2} - (5 + 2 i) z = 0

2 z^{2} + (- 2 - 2 i) z - 6 + 9 i = 0

a + bi - \frac{1}{a + bi} = 4 + 4 i

i (a + bi - 5) = (1 + 3 i) (a + bi)

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

What is the answer to (a+bi)^2=(a+b)(a-b)+2abi ?
The answer to (a+bi)^2=(a+b)(a-b)+2abi is No Solution