Dividing complex numbers
7-13i/2i
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To divide complex numbers, you use the same principle as dividing real numbers. The only difference is that to simplify the expression, you'll need to multiply the numerator and denominator by the conjugate of the denominator.
Let's apply this principle to the given expression:
To divide (7 - 13i) by (2i), we first find the conjugate of the denominator, which is (-2i).
Next, multiply both the numerator and denominator by the conjugate (-2i) to create an equivalent expression that has a real denominator.
(7 - 13i) / (2i) * (-2i) / (-2i)
We multiply the numerators (7 - 13i) * (-2i) = (14i -26)
We multiply the denominators (2i) * (-2i) = -4i²
Remember that i² is equal to -1, so -4i² becomes -4*(-1) = 4
Therefore, the expression simplifies to:
(14i -26) / 4
You can further simplify this expression by dividing both the numerator and denominator by 2.
(14i -26) / 4 = (7i - 13) / 2
So, the final answer is (7i - 13) / 2.
(7-13i)/(2i)
= (7-13i)/(2i) * i/i
= (7i - 13i^2)/(2i^2) , remember i^2 = -1
= (7i + 13)/-2
= (-13 - 7i)/2
check my arithmetic