What is the answer to x^2=1184+125.6637i ?

The answer to x^2=1184+125.6637i is

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x^2=1184+125.6637i

x^{2} = 1184 + 125.6637 i

x = \frac{11840000 + 1.41765 E 14}{100 2} + \frac{6283.185 2}{11840000 + 1.41765 E 14} i, x = - \frac{11840000 + 1.41765 E 14}{100 2} - \frac{2 \cdot 6283.185}{11840000 + 1.41765 E 14} i

Solution steps

x^{2} = 1184 + 125.6637 i

Substitute

x = a + bi

(a + bi)^{2} = 1184 + 125.6637 i

Expand

(a + bi)^{2} : (a^{2} - b^{2}) + 2 iab

(a^{2} - b^{2}) + 2 iab = 1184 + 125.6637 i

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

[a^{2} - b^{2} = 1184 2 ab = 125.6637]

[a^{2} - b^{2} = 1184 2 ab = 125.6637] : a = \frac{11840000 + 1.41765 E 14}{100 2}, a = - \frac{11840000 + 1.41765 E 14}{100 2}, b = \frac{6283.185 2}{11840000 + 1.41765 E 14} b = - \frac{2 \cdot 6283.185}{11840000 + 1.41765 E 14}

Substitute back

x = a + bi

x = \frac{11840000 + 1.41765 E 14}{100 2} + \frac{6283.185 2}{11840000 + 1.41765 E 14} i, x = - \frac{11840000 + 1.41765 E 14}{100 2} - \frac{2 \cdot 6283.185}{11840000 + 1.41765 E 14} i

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