We check this result for z = e7πi / 6: z = e7πi / 6 = − √3 2 − 1 2i. z2 = 1 2 + √3 2 i; iz2 = − √3 2 + 1 2i = ˉz; a similar calculation validates z = e11πi / 6. It is easy to see that i(i)2 = − i and the solution z = 0 "checks itself", as it were. The complete solution set is thus. {0, i, e7πi / 6, e11πi / 6}. Suppose, z = a+ib is a complex number. Then, the modulus of z will be: |z| = √(a 2 +b 2), when we apply the Pythagorean theorem in a complex plane then this expression is obtained. Hence, mod of complex number, z is extended from 0 to z and mod of real numbers x and y is extended from 0 to x and 0 to y respectively. The absolute value of a number is often viewed as the "distance" a number is away from 0, the origin. For real numbers, the absolute value is just the magnitude of the number without considering its sign. For example, the absolute value of -5 is 5, and the absolute value of 5 is also 5. For a complex number So this is the conjugate of z. So just to visualize it, a conjugate of a complex number is really the mirror image of that complex number reflected over the x-axis. You can imagine if this was a pool of water, we're seeing its reflection over here. And so we can actually look at this to visually add the complex number and its conjugate. Here z = a + ib z = a + i b ie. z = (a, b) z = ( a, b) and can be represented as a point or vector on complex plane above. |z|2 =a2 +b2 = 1 | z | 2 = a 2 + b 2 = 1. and this itself is a locus of a circle. would you mind if I draw your graphic in TikZ ? yours look so much like paint. Equation of a line in complex form. The question is to find out the equation of two lines making an angle 45° 45 ° with a given line a¯z + az¯ + b = 0 a ¯ z + a z ¯ + b = 0 (where a a is a complex number and b b is real) and passing through a given point c c is ( c c is a complex number) Writing z z as x + iy x + i y we get the slope of jSUu.

z bar in complex numbers