Complex numbers
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Deleted member 4993
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Dr.Peterson
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No, nothing is obvious. In fact, there is no question there! A few words are needed, to say what your goal is, and what each step you took means. Please read our submission guidelines. Following them really does help us answer more effectively.
It appears that you are trying to express [MATH]\sqrt{1 + \sqrt{i}}[/MATH] in [MATH]a + bi[/MATH] form. (But I would not really call that "such an easy problem"!) Then you seem to be finding [MATH]\sqrt{i}[/MATH] in exponential (polar) form.
Since addition doesn't work well in polar form, you might want to go back to rectangular ("general") form, as you almost did, in order to add, and then revert to polar form for the next root. What is [MATH]\cos{\pi/4}[/MATH]?
There are other ways you might do it; I suppose your context (having been learning to use exponential form?) suggests the method you are using.
It appears that you are trying to express [MATH]\sqrt{1 + \sqrt{i}}[/MATH] in [MATH]a + bi[/MATH] form. (But I would not really call that "such an easy problem"!) Then you seem to be finding [MATH]\sqrt{i}[/MATH] in exponential (polar) form.
Since addition doesn't work well in polar form, you might want to go back to rectangular ("general") form, as you almost did, in order to add, and then revert to polar form for the next root. What is [MATH]\cos{\pi/4}[/MATH]?
There are other ways you might do it; I suppose your context (having been learning to use exponential form?) suggests the method you are using.
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What does "amount" mean - with reference to this problem?
pka
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If it obvious then here is an obvious answer.