Recall the symbol Z represents the complex conjugate of z. If z=a+bi and w=c+di show that the statement is true zw=z*w

Question

Heath Boyd

Mathematics

8 May, 13:53

Recall the symbol Z represents the complex conjugate of z. If z=a+bi and w=c+di show that the statement is true zw=z*w

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Mia Booker · Answer 1

Z = a + bi

w = c + di

zw = (a + bi) (c + di)

zw = a (c + di) + bi (c + di)

zw = a (c) + a (di) + bi (c) + bi (di)

zw = ac + adi + bci + bdi²

zw = ac + adi + bci + bd (-1)

zw = ac + adi + bci - bd