SOLUTION: Write the complex number (3 - i)/(i + 2) in the standard form a + bi, with a and b in fractional form.

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Question 638507: Write the complex number (3 - i)/(i + 2) in the standard form a + bi, with a and b in fractional form.
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
The standard form does not allow for complex numbers to be at the denominator.
The standard form is:
a+%2B+bi
We'll have to get the complex number out of the denominator. For this reason,
we'll have to multiply the numerator and denominator by the conjugate of the
denominator: %28i+-+2%29+.



=%283i-6+-+i%5E2%2B2i%29%2F%28i%5E2-2i+%2B+2i-4+%29

=%285i-6+-+%28-1%29%29%2F%28%28-1%29-cross%282i%29+%2B+cross%282i%29-4+%29

=+%285i-6+%2B1%29%2F%28-1-4+%29

=+%285i-5%29%2F%28-5+%29
The standard form is:
a+%2B+bi=+5i%2F-5+-+5%2F-5
=+-i+%2B1
=1-i+