# Using the rules of multiplication of complex numbers, what is the result (5+2i)(2-i)?

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The result of (5+2i)(2-i) can be found by opening the brackets and multiplying the terms.

(5 + 2i)(2 - i)

=> 10 - 5i + 4i - 2i^2

we know that i^2 = -1

=> 10 - 5i + 4i + 2

=> 12 - i

**The result is (5+2i)(2-i) = 12 - i**

We'll explain the multiplication of complex numbers written in algebraic form, choosing 2 comeplx numbers:

z1 = 5+2i and z2 = 2-i

The real part of z1 = Re(z1) = 5

The imaginary part of z1 = Im(z1) = 2

The real part of z2 = Re(z2) = 2

The imaginary part of z2 = Im(z2) = -1

We'll multiply the numbers z1*z2 = (5+2i)(2-i)

We'll apply FOIL:

z1*z2=10-5i+4i-2i^2

i^2 = -1

**The result of (5+2i)(2-i) is z1*z2 = 12 - i**