Answer:
26+13i
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