# cosh(x)

1. Real function z = f(x,y) in the real space :
2. Real function z = f(x) on the real axis x is cross-section in above figure on y-axis when y=0 :
3. Complex function re(z) = f(x,y), Real part of complex value in the real space :
4. Complex function z = re(z) + im(z) i, re(z) = f(x) and im(z) = f(x), Real (blue) + imaginary (red) part on the real axis x is cross-section in above figure on y-axis when y=0 :
5. re(z) = f(complex(x,y)), Real part of complex value in the complex plane :
6. re(z) = f(complex(x)), Real part of complex value on the real axis x is cross-section on y axis in above figure. It is the same as Figure 4 when y=0.
7. re(z) = f(complex(y)), Real part of complex value on the imaginary axis y is cross-section on x axis:
8. im(z) = f(x,y), Imaginary part of complex value in the real space :
9. im(z) = f(x), Imaginary part of complex value on the real axis x is cross-section in above figure on y-axis when y=0 :
10. im(z) = f(complex(x,y)), Imaginary part of complex value on the complex plane:
11. im(z) = f(complex(x)), Imaginary part of complex value on the real axis x is cross-section on y axis in above figure. It is the same as Figure 9 when y=0.
12. im(z) = f(complex(y)), Imaginary part of complex value on the imaginary axis y is cross-section on x axis:
13. z = figure 6 + figure 10 = re(z)+ im(z) i = Real (blue) + imaginary (red) part of complex value on the real axis x is cross-section on y axis in above figure. It is the same as Figure 4 when y=0:
14. z = figure 7 + figure 12 = re(z) + im(z) i = Real (blue) + imaginary (red) part of complex value on the imaginary axis y is cross-section on x axis:
15. abs(z) = f(complex(x,y)), Absolute value of complex value on the complex plane:

## Reference

• Function category: complex functions
• Function category: complex math