Question

(-7i)(3+3i)(a) Write the trigonometric forms of the complex numbers. (Let0 ≤ theta < 2pi.)(-7i) =(3+31) =(b) Perform the indicated operation using the trigonometric forms. (Let0 ≤ theta< 2pi.)(c) Perform the indicated operation using the standard forms, and check your result with that of part (b).

Answer 1

A complex number z is given in the form:

z = (x.y) = (realpart) x + imaginary part (iy)

In this case:

z1 = -7i

z2 = 3+3i

To write in trigonometric form:

Multiplication in trigonometric form:

`z1*z2\text{ = \lparen21}√(2)\text{ \rparen \lparen cos}(7\pi)/(4);\text{ sin}(7\pi)/(4))`

Multiplication in standard form:

`\begin{gathered} (-7i)(3\text{ + 3i\rparen} \\ =-21i\text{ - 21i}^2 \\ i^2\text{ = -1} \\ =\text{ -21i + 21} \\ r\text{ = }√(21^2+21^2) \\ =21√(2) \end{gathered}`