complex number combined sum of a real number and an imaginary number. the basic expression of complex number is a + bi.(a and b are real numbers) An imaginary number is a multiple of i, it mean i is $ \sqrt-1 $.

for example of complex number.

calculate this.

$ (4+3\sqrt2i)-(2-\sqrt2i) $

answer:

       $ = 4+3\sqrt2i - 2+\sqrt2i $
       $ = (4-2) + (3\sqrt2 + \sqrt2)i $
       $ =2 + 4\sqrt2i $

another example,

change to $ a+bi $ form.

$ ((1+i)/(1-i))^4 $

answer:

         $ =\left(\frac{\left(1+i\right)^2}{\left(1-i\right)\times\left(1+i\right)}\right)^4 $
       
          $ =\left(\frac{1+2i+\left(i\right)^2}{1^2-\left(i\right)^2}\right)^4 $
       
          $ =\left(\frac{1+2i-1}{1-\left(-1\right)}\right)^4 $
       
          $ =\left(\frac{2i}{2}\right)^4 $
       
          $ =i^4 $
       
          $ =((i)^2)^2 $
       
          $ =(-1)^2=1 $
       
          $ =1 + 0i $

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