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How to find the complex number 1-I / 2I? First, what number does I represent
I is an imaginary unit
i^2= -1
First, multiply the fraction up and down by 1 + I
Original formula = 2I (1 + I) / (1-I) (1 + I)
=（2i+2i^2）/（1-i^）
=（2i-2）/2
=i-1
|The complex Z satisfies | Z-3 | + | Z + 3 | = 10, and | z-5i | - | Z + 5I | = 8
For example, | Z-3 | + | Z + 3 | = 10 means that the sum of distances from Z to (3,0) (- 3,0) is 10, means that z is an ellipse with (3,0), (- 3,0) as the focus and the length of its major axis is 5, and the equation is x ^ 2 / 25 + y ^ 2 / 16 = 1; similarly, | z-5i | - | Z + 5I | = 8 means that the distance difference between Z and (0,5) (0, - 5) is 8
Given that the real part of complex Z is - 1 and the imaginary part is 2, then 5iz is equal to______ ．
∵ the real part of complex Z is - 1, the imaginary part is 2, ∵ z = - 1 + 2I, ∵ 5iz = 5I − 1 + 2I = 5I (− 1 − 2I) (− 1 + 2I) (− 1 − 2I) = 2-I, so the answer is: 2-i
Given that the complex Z of 0 satisfies that (2 + 3I) Z equals 4z-5i, then Z equals 0
Z=-(15/13)+(10/13)i
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