What is the answer to (1+i)z^2=-1+7 ?

The answer to (1+i)z^2=-1+7 is No Solution

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(1+i)z^2=-1+7

(1 + i) z^{2} = - 1 + 7

No Solution

Solution steps

(1 + i) z^{2} = - 1 + 7

Substitute

z = x + y i

(1 + i) (x + y i)^{2} = - 1 + 7

Expand

(x^{2} - y^{2} - 2 x y) + i (x^{2} - y^{2} + 2 x y) = 6

Rewrite

6

in standard complex form:

6 + 0 i

(x^{2} - y^{2} - 2 x y) + i (x^{2} - y^{2} + 2 x y) = 6 + 0 i

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

[x^{2} - y^{2} - 2 x y = 6 x^{2} - y^{2} + 2 x y = 0]

[x^{2} - y^{2} - 2 x y = 6 x^{2} - y^{2} + 2 x y = 0] : No Solution

Substitute back

z = x + y i

No Solution

(x + i y)^{2} + (1 + 4 i) (x + i y) = 5 + i

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

x - y i = 4 + 7 i

\frac{1}{i C} = - 0.035 i

x + i y + i x + y = 2 + i

What is the answer to (1+i)z^2=-1+7 ?
The answer to (1+i)z^2=-1+7 is No Solution