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Given real number input, the function behaves like the cosine function. Related functions IMSIN Function The Excel IMSIN function returns the sine of a complex number. COMPLEX Function The Excel COMPLEX function returns the string representation of a complex number. IMREAL Function The Excel IMREAL function returns the real part of a complex number. IMAGINARY Function The Excel IMAGINARY function returns the imaginary part of a complex number. COS Function The Excel COS function returns the cosine of an angle given in radians....

Given “1+1.5707963267949i” as input, the function returns “-5.4E-15+1.175201i” as output. The imaginary output along the imaginary axis traces the shape of theCOSfunction. Explanation The function can be defined using theCOSH,COS,SINH, andSINfunctions. Related functions COSH Function The Excel COSH function returns the hyperbolic cosine of a number. IMSINH Function The Excel IMSINH function returns the hyperbolic sine of a complex number.

For example, given “3+4i” as input, the function returns “-0.000187588-1.000644392i” as output. In Excel, the cotangent of a complex number is equivalent to the following formula. The cotangent is the reciprocal of thecomplex tangent function. Related functions IMTAN Function The Excel IMTAN function returns the tangent of a complex number. … IMCOS Function The Excel IMCOS function returns the cosine of a complex number. IMSIN Function The Excel IMSIN function returns the sine of a complex number....

For example, given “4+3i” as input, the function returns “-0.075489833+0.064877471i” as output. Explanation In math, the complex cosecant function is the reciprocal of thecomplex sine function. In Excel, the complex cosecant function is equivalent to the following formula. Related functions IMSIN Function The Excel IMSIN function returns the sine of a complex number.

Given “1+1.5707963267949i” as input, the function returns “-1.72324E-15-0.648054274i” as output. Explanation The complex hyperbolic cosecant function is the reciprocal of the complex hyperbolic sine function. In Excel, the function’s output is equivalent to the following formula. CSC Function CSCH Function The Excel CSCH function returns the hyperbolic cosecant of an angle.

We can visualize the example that corresponds to this one by switching the divisor with the quotient. Explanation When dividing complex numbers, it’s not obvious how to calculate the result by hand. Compare this to complex multiplication, where we can use algebra to multiply two complex numbers. The key to dividing two complex numbers is to convert the problem into one we know how to solve. This is done by using the fact that multiplying a complex number by its conjugate equals a real number....

For example, given “0+i” as input, the function returns “-1+3.23108914886517E-15i” as output. Given real number input, the function behaves like the exponential function and models exponential growth. Notation The complex exponential function often appears as the Latin letter e to some power. This notation is equivalent to passing the complex number as input to the exponential function. We can write another version of this formula that better describes what’s happening in terms of the angle ....

The 3D graph below visualizes the imaginary part of the function’s output. Geometrically, the imaginary part equals the angle in radians of the complex number output by the function. The difference is because of the exponential function’s periodic nature. For example, consider a complex number written in terms of its radius and angle (polar form). The angle that describes the number can take on infinitely many values. Because if you add 2 to any angle, you get an equivalent complex number....

In Excel, we can define the base-10 logarithm using the following formula. See theIMLNfunction for a more in-depth explanation of the complex logarithm. IMLN Function The Excel IMLN function returns the natural logarithm of a complex number. IMLOG2 Function The Excel IMLOG2 function returns the base-2 logarithm of a complex number. LOG10 Function The Excel LOG10 function returns the base 10 logarithm of a number. For example, LOG10(100) returns 2, and LOG10(1000) returns 3....

For example, given the “-4i” input, the function returns “2-2.2661800709136i” as output. In Excel, we can define the complex base-2 logarithm using the following formula. See theIMLNfunction for a more in-depth explanation of complex logarithms. IMLOG10 Function The Excel IMLOG10 function returns the base-10 logarithm of a complex number. The base argument defaults to 10 if not supplied.

Implicit Intersection describes a formula behavior in Excel where many values are reduced to a single value. In other words, entering a formula with control + shift + enter disables implicit intersection. For example, if same formula above is entered in cell D9, the result is #VALUE. This makes it possible to create formulas that manipulate multiple values input as ranges. This @ symbol is called the implicit intersection operator, and itdisablesarray behavior....

IMREAL Function The Excel IMREAL function returns the real part of a complex number. IMAGINARY Function The Excel IMAGINARY function returns the imaginary part of a complex number.

For example: Excel handles complex numbers as strings formatted like “x+yi” or “x+yj”. Use theCOMPLEXfunction to get the string representing a complex number. Arguments can be hard-coded values, cell references, or a range. Let’s visualize another example. IMREAL Function The Excel IMREAL function returns the real part of a complex number. IMAGINARY Function The Excel IMAGINARY function returns the imaginary part of a complex number. IMDIV Function The Excel IMDIV function returns the quotient of two complex numbers....