Question 1038209: Simplify 3+5i/2i
Found 2 solutions by Othel, josgarithmetic:
Answer by Othel(27)   (Show Source):
You can put this solution on YOUR website! When dividing complex numbers, we multiply the numerator and denominator by something called the complex conjugate of the denominator. Long words for a simple idea. Basically, it is the negative of the complex number in the divisor. By doing this, we eliminate the complex number, and are left with a positive, real number denominator, where we started out with a complex number. So...
(3 + 5i)/2i * (-2i)/(-2i) = (10-6i)/4
Which reduces to
(5 - 3i)/2, or 5/2 - 3i/2
On the bottom, 2i * -2i = (-4)(i^2). Working with complex numbers, you must know that i^2 is -1. So this expression is equal to (-4)(-1). Which equals 4.
And on the top, (3)(-2i) = -6i, and (5i)(-2i) = (-10)(i^2) = (-10)(-1) = 10
Hope this helps! Learn on
Answer by josgarithmetic(39615) (Show Source):
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