Use trigonometric forms to find z1z2 and z1/z2.

Question

Use trigonometric forms to find z₁z₂ and z₁/z₂. (Enter your answers in the form a + bi.)

z₁ = −5 + 5i,    z₂ = 5 + 5i

z₁z_{2= ?}

z_1/z_{2= ?}

Answer 1

z₁ = 5√2(cos3π/4 + isin3π/4); z₂ = 5√2(cosπ/4 + isinπ/4).

z₁z₂ = 50(cosπ + isinπ) = - 50

z₁/z₂ = cosπ/2 + isinπ/2 = i

Answer 2

First of all move the minus sign in the numerator out from and then divide out the 5 so that you have

-(1-i)/(1+i)

Now multiply the numerator and denominator (both) by 1-i to get

1(1-i)²/2

You can now expand the numerator to get a form like a+bi...just remember to being along the 2 in the denominator!