Im(z)和Re(z)是什么意思他们分别代表复数的虚数部分和实数部分，比如： Z=a+bi，则 ReZ=a， ImZ=b。虚数 ImagicNumber实数 RealNumber符号分别是取了前两个字母。有理数是伴随人们的生产实践而产生的。无理数的发现

Two complex numbers $z_1$ and $z_2$ so that $z_1=kz_2 \iff z_1 \bar{z_2} \in \Bbb R^+$ 0 Showing that $f(z) = e^z$ for $z = x + iy$ is injective when $-1 \leq x \leq 1, 0 \leq y \leq \pi$

The complex conjugate of a complex number z is written z *. Notice that z + z * = 2Re{z}, z - z * = 2iIm{z}. Hence, the real and imaginary parts can be obtained using the complex conjugate, Re{z} = (z + z *) / 2, Im{z} = (z - z *) / 2i. Products The product of two complex numbers works as expected if you remember that i 2 = -1. So, for example,

A complex number z = (x,y), or as z = x + iy, is defined by a pair of real numbers x and y; so does for a point (x,y) in the x-y plane. We associate a one-to-one correspondence between the complex number z = x + iy and the point (x,y) in the x-y plane. We refer the plane as the complex plane or z-plane. 2

The real part of z, denoted Re(z), is equal to x; the imaginary part of z, de- noted Im( z ), is equal to y . Notice that both Re( z ) and Im( z ) are real numbers.

2019年10月16日 · If you ''accept'' complex conjugation, then $$\Re(z)=\frac{z+\overline{z}}{2}$$ and $$\Im(z)=\frac{z-\overline{z}}{2i}$$

If z = x +iy ; its conjugate is z = x iy : Properties: z +w = z +w zw = z w z +z = 2Re(z); z z = 2i Im(z) If z = x +iy ; then z z = x2 +y2 If z = x +iy ; w = u +iv then Re(zw) = xu +yv = (x;y)(u;v) dot product

复数 定义1： 一对有序数对 (u,v) ； z=u+iv . u=\operatorname {Re}z 称为 实部， v=\operatorname {Im} 称为 虚部。 复数定义2（复数的指数形式）： z=re^ {iθ}=r (\cosθ+ i\sinθ) （Euler 公式） 【本质上是借助 Taylor 展开式： e^ {iθ}=\sum\limits_ {n=0}^\infty \dfrac { (iθ)^n} {n!}=\cos θ+i\sin θ 】 性质： e^ {i (θ_1+θ_2)}=e^ {iθ_1}\cdot e^ {iθ_2} e^ {iθ}=e^ {i (θ+2kπ)} 以 2π …

2017年2月8日 · In texts on complex numbers I often see an exercise that asks to prove the following: $$Re (z) = \frac {z + z^*} {2}$$ $$Im (z) = \frac {z − z^*} {2i}$$ where $z = x + iy$ and $z^* = x - iy$ I unders...

2016年11月13日 · z=x+iy，表复数 Re(z)=x 表示复数z的实部 Im(z)=y 表示复数z的虚部