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[tex]i=\sqrt{-1}\to i^2=-1\\\\i^{39}=i^{38+1}=i^{38}\cdot i^1=i^{2\cdot19}\cdot i=(i^2)^{19}i=(-1)^{19}i=-1i=-1\\\\Used:\\\\a^n\cdot a^m=a^{n+m}\\\\(a^n)^m=a^{n\cdot m}[/tex]

The given expression is equivalent to -i

What is complex number?

A complex number is a combination of real values and imaginary values. It is denoted by z = a + ib, where a, b are real numbers and i is an imaginary number.

Let [tex]z=i^{39}[/tex]

[tex]i^2=-1[/tex]

[tex]z= i^{38}.i\\z=(i^{2})^{19}.i\\z=(-1)^{19}.i\\z=-i[/tex]

Learn more about complex number

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