What are the solutions to the equation (400+j^{1000})I^2-j^{90}I^1=0 ?

The solutions to the equation (400+j^{1000})I^2-j^{90}I^1=0 are I=(j^{90})/(400+j^{1000)},I=0

Find the zeros of (400+j^{1000})I^2-j^{90}I^1=0

The zeros of (400+j^{1000})I^2-j^{90}I^1=0 are I=(j^{90})/(400+j^{1000)},I=0

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(400 + j^{1000}) I^{2} - j^{90} I^{1} = 0

I = \frac{j ^{90}}{400 + j ^{1000}}, I = 0

Solution steps

(400 + j^{1000}) I^{2} - j^{90} I^{1} = 0

Expand

(400 + j^{1000}) I^{2} - j^{90} I^{1} : 400 I^{2} + j^{1000} I^{2} - j^{90} I

400 I^{2} + j^{1000} I^{2} - j^{90} I = 0

Write in the standard form

a x^{2} + b x + c = 0

(400 + j^{1000}) I^{2} - j^{90} I = 0

Solve with the quadratic formula

I_{1, 2} = \frac{- ( - j ^{90} ) \pm ( - j ^{90} ) ^{2} - 4 ( 400 + j ^{1000} ) \cdot 0}{2 ( 400 + j ^{1000} )}

Simplify

(- j^{90})^{2} - 4 (400 + j^{1000}) \cdot 0 : j^{90}

I_{1, 2} = \frac{- ( - j ^{90} ) \pm j ^{90}}{2 ( 400 + j ^{1000} )}

Separate the solutions

I_{1} = \frac{- ( - j ^{90} ) + j ^{90}}{2 ( 400 + j ^{1000} )}, I_{2} = \frac{- ( - j ^{90} ) - j ^{90}}{2 ( 400 + j ^{1000} )}

I = \frac{- ( - j ^{90} ) + j ^{90}}{2 ( 400 + j ^{1000} )} : \frac{j ^{90}}{400 + j ^{1000}}

I = \frac{- ( - j ^{90} ) - j ^{90}}{2 ( 400 + j ^{1000} )} : 0

The solutions to the quadratic equation are:

I = \frac{j ^{90}}{400 + j ^{1000}}, I = 0

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What are the solutions to the equation (400+j^{1000})I^2-j^{90}I^1=0 ?
The solutions to the equation (400+j^{1000})I^2-j^{90}I^1=0 are I=(j^{90})/(400+j^{1000)},I=0
Find the zeros of (400+j^{1000})I^2-j^{90}I^1=0
The zeros of (400+j^{1000})I^2-j^{90}I^1=0 are I=(j^{90})/(400+j^{1000)},I=0