(4+7i)(3-2i)

⚪ 2+9i
⚪ 2-9i
⚪ 26+13i
⚪ 26-13i​

26+13i

Step-by-step explanation:

(4+7i)(3−2i)

Multiply complex numbers 4+7i and 3−2i like you multiply binomials.

4×3+4×(−2i)+7i×3+7(−2)i^2

By definition, i^2  is −1.

4×3+4×(−2i)+7i×3+7(−2)(−1)

Do the multiplications.

12−8i+21i+14

Combine the real and imaginary parts.

12+14+(−8+21)i

Do the additions.

26+13i

Real part steps:

(4+7i)(3−2i)

Multiply complex numbers 4+7i and 3−2i like you multiply binomials.

Re(4×3+4×(−2i)+7i×3+7(−2)i^2)By definition, i^2 is −1.

Re(4×3+4×(−2i)+7i×3+7(−2)(−1))

Do the multiplications in 4×3+4×(−2i)+7i×3+7(−2)(−1).

Re(12−8i+21i+14)

Combine the real and imaginary parts in 12−8i+21i+14.

Re(12+14+(−8+21)i)

Do the additions in 12+14+(−8+21)i.

Re(26+13i)

The real part of 26+13i is 26.

26