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Complex numbers question
How would we solve e^z = -1 ?
I did this
e^z = -1
let z = a+bi
e^(a+bi) = -1
e^a * e^(bi) = -1
e^a( cosb + isinb) = -1
Now what? Or should I be using the natural logarithm?
EDIT: Actually, could I just put -1 in exponential form and then log both sides?
I did this
e^z = -1
let z = a+bi
e^(a+bi) = -1
e^a * e^(bi) = -1
e^a( cosb + isinb) = -1
Now what? Or should I be using the natural logarithm?
EDIT: Actually, could I just put -1 in exponential form and then log both sides?
Oh yeah Euler's identity.... I should have recognized it. Thanks. I have the answer. Though my method of putting the RHS in exponential form will work with any question like this.
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