What is the answer to 0=10^5(10+ix)(1000+ix) ?

The answer to 0=10^5(10+ix)(1000+ix) is x=1000i,x=10i

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0=10^5(10+ix)(1000+ix)

0 = 1 0^{5} (10 + i x) (1000 + i x)

x = 1000 i, x = 10 i

Solution steps

0 = 1 0^{5} (10 + i x) (1000 + i x)

Substitute

x = a + bi

0 = 1 0^{5} (10 + i (a + bi)) (1000 + i (a + bi))

Expand

1 0^{5} (10 + i (a + bi)) (1000 + i (a + bi)) : (- 100000 a^{2} - 101000000 b + 100000 b^{2} + 1000000000) + i (101000000 a - 200000 ab)

0 = (- 100000 a^{2} - 101000000 b + 100000 b^{2} + 1000000000) + i (101000000 a - 200000 ab)

Rewrite

0

in standard complex form:

0 + 0 i

0 + 0 i = (- 100000 a^{2} - 101000000 b + 100000 b^{2} + 1000000000) + i (101000000 a - 200000 ab)

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

[0 = - 100000 a^{2} - 101000000 b + 100000 b^{2} + 1000000000 0 = 101000000 a - 200000 ab]

[0 = - 100000 a^{2} - 101000000 b + 100000 b^{2} + 1000000000 0 = 101000000 a - 200000 ab] : (a = 0, a = 0, b = 1000 b = 10)

Substitute back

x = a + bi

x = 1000 i, x = 10 i

- x^{2} = 2 i

x^{2} = 1184 + 125.6637 i

2 w^{2} + (- 6 + 7 i) w - 11 + 2 i = 0

x^{2} + (2 - 2 i) x - (4 + 2 i) = 0

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

What is the answer to 0=10^5(10+ix)(1000+ix) ?
The answer to 0=10^5(10+ix)(1000+ix) is x=1000i,x=10i