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Aus Online Mathematik Brückenkurs 2

We expand the expression by multiplying each term in the first bracket with every term in the second bracket,

(3−2i)(7+5i)=37+35i+=37+35i−2i7−2i5i.

Then, we use that i2=−1 and write the real and imaginary parts together,

(3−2i)(7+5i)=21+15i−14i−10i2=21+15i−14i−10(−1)=(21+10)+(15i−14i)=31+(15−14)i=31+i.