starrhunter
rationalize the denominator of
√-16
_________
(1+i)+(6+3i)
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m_charron2
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-16 can be written as the product of 16 and -1, right? so what's the sqrt of 16 and the sqrt of -1?
starrhunter
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i haven't any idea
hashsam1
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|dw:1337100713360:dw|
m_charron2
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ok, sqrt of 16, what multiplied with itself gives 16?
starrhunter
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4
m_charron2
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ok, what about -1?
starrhunter
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im not sure about the -1
starrhunter
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there isnt an answer for that... right?
hashsam1
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|dw:1337100894030:dw|
m_charron2
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ok, I'll give you that one, because it's a bit tricky, it's actually i. i * i = -1
starrhunter
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i times i. got it.
m_charron2
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ok, perfect, so sqrt of -16 = sqrt 16 * sqrt -1 = 4 * i
starrhunter
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but its negative 16 under the square root....
starrhunter
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and none of that is one of my choices
starrhunter
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all of my choices look like fractions
m_charron2
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Yup, and it's still works because of this :
\[\sqrt{xy} = \sqrt{x} * \sqrt{y}\]
right, so once you solve the the denominator, go back to hashsam1's solution
hashsam1
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|dw:1337101077852:dw|
starrhunter
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so it would be
hashsam1
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|dw:1337101138650:dw|
starrhunter
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thank you so much for all of your help!
hashsam1
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is this the answer?
hashsam1
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in your choices?
starrhunter
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its 16 + 28i over 65
m_charron2
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perfect
starrhunter
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|dw:1337101312782:dw|
starrhunter
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yay!
hashsam1
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|dw:1337101388901:dw|