Solve I 1 + I^2 + I^3 + I^4 = 0

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Type your math problem... I 1 + I^2 + I^3 + I^4 = 0

Question

Solve the equation

I_{1} = - 1, I_{2} = 0

Evaluate

I \times 1 + I^{2} + I^{3} + I^{4} = 0

Any expression multiplied by 1 remains the same

I + I^{2} + I^{3} + I^{4} = 0

Factor the expression

I (1 + I) (1 + I^{2}) = 0

Separate the equation into 3 possible cases

I = 0 1 + I = 0 1 + I^{2} = 0

Solve the equation

More Steps

Evaluate

1 + I = 0

Move the constant to the right-hand side and change its sign

I = 0 - 1

Removing 0 doesn't change the value,so remove it from the expression

I = - 1

I = 0 I = - 1 1 + I^{2} = 0

Solve the equation

More Steps

Evaluate

1 + I^{2} = 0

Move the constant to the right-hand side and change its sign

I^{2} = 0 - 1

Removing 0 doesn't change the value,so remove it from the expression

I^{2} = - 1

Since the left-hand side is always positive or 0,and the right-hand side is always negative,the statement is false for any value of I

I \in / R

I = 0 I = - 1 I \in / R

Find the union

I = 0 I = - 1

Solution

I_{1} = - 1, I_{2} = 0

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