Define a 3-by-4 matrix, A.

A = [7 3+4i 2 5i;...
     2i 1+3i 12 345;...
     52 108 78 3];

Determine whether the array is real.

tf = isreal(A)

tf = logical
   0

Since A contains complex elements, isreal returns false.

Use the complex function to create a scalar, A, with zero-valued imaginary part.

A = complex(12)

A = 12.0000 + 0.0000i

Determine whether A is real.

tf = isreal(A)

tf = logical
   0

A is not real because it has an imaginary part, even though the value of the imaginary part is 0.

Determine whether A contains any elements with zero-valued imaginary part.

~any(imag(A))

ans = logical
   1

A contains elements with zero-valued imaginary part.

Define two complex scalars, x and y.

x=3+4i;
y=5-4i;

Determine whether the addition of two complex scalars, x and y, is real.

A = x+y

A = 8

MATLAB® drops the zero imaginary part.

isreal(A)

ans = logical
   1

A is real since it does not have an imaginary part.

Create a cell array.

C{1,1} = pi;                 % double
C{2,1} = 'John Doe';         % char array
C{3,1} = 2 + 4i;             % complex double
C{4,1} = ispc;               % logical
C{5,1} = magic(3);           % double array
C{6,1} = complex(5,0)        % complex double

C=6×1 cell array
    {[          3.1416]}
    {'John Doe'        }
    {[2.0000 + 4.0000i]}
    {[               0]}
    {3x3 double        }
    {[5.0000 + 0.0000i]}

C is a 1-by-6 cell array.

Loop over the elements of a cell array to distinguish between real and complex elements.

for k = 1:6
x(k,1) = isreal(C{k,1});
end

x

x = 6x1 logical array

   1
   1
   0
   1
   1
   0

All but C{3,1} and C{6,1} are real arrays.