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A to Z of Excel Functions: the IMCSC Function

24 August 2020

Welcome back to our regular A to Z of Excel Functions blog.  Today we look at the IMCSC function.

 

The IMCSC function

An imaginary number is a complex number that can be written as a real number multiplied by the imaginary unit i (sometimes denoted j) which is defined by its property i2 = −1.  In general, the square of an imaginary number bi is −b2.  For example, 9i is an imaginary number, and its square is −81.  Zero is considered to be both real and imaginary.

An imaginary number bi can be added to a real number a to form a complex number of the form a + bi, where the real numbers a and b are called, respectively, the real part and the imaginary part of the complex number.

The polar form of a complex number is another way to represent the number.  The form z = a + bi is called the rectangular form of a complex number.

The horizontal axis is the real axis and the vertical axis is the imaginary axis.  You can find the real and imaginary components in terms of r and θ, where r is the length of the vector and θ is the angle made with the real axis.

From the Pythagorean Theorem,

r2 = a2 + b2

By using the basic trigonometric ratios,

cos θ = a / r and sin θ = b / r

Therefore, multiplying each side by r:

r cos θ = a and r sin θ = b

Therefore,

z = a + bi

<=> z = r cos θ + (r sin θ)i

<=> z = r(cos θ + i sin θ)

In the case of a complex number, represents the absolute value, or modulus (where r = |z| = (a2+b2)), and the angle θ is called the argument of the complex number (θ = tan-1(b/a) for > 0 and θ = tan-1(b/a) + π for a < 0).

The cosecant is simply the reciprocal of the sine function.  The IMCSC function returns the cosecant of a complex number in x + yi or x + yj text format.

The IMCSC function employs the following syntax to operate:

IMCSC(inumber)


The IMCSC function has the following argument:

  • inumber: this is required and represents the complex number for which you want to calculate the cosecant.

It should be further noted that:

  • you should use COMPLEX to convert real and imaginary coefficients into a complex number
  • IMCSC recognises either the i or j notation
  • if inumber is a value that is not in the x + yi or x + yj text format, IMCSC returns the #NUM! error value
  • if inumber is a logical value, IMCSC returns the #VALUE! error value
  • if the complex number ends in +i or -i (or j), i.e. there is no coefficient between the operator and the imaginary unit, there must be no space, otherwise IMCSC will return an #NUM! error.

Please see my example below: 

 

 

We’ll continue our A to Z of Excel Functions soon.  Keep checking back – there’s a new blog post every business day.

A full page of the function articles can be found here

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