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z= 8 - 9iFind the angle (in radians) that makes in the complex plane.Round your answer, if necessary, to the nearest thousandth. Express 0 between -T and T.

Z 8 9iFind The Angle In Radians That Makes In The Complex PlaneRound Your Answer If Necessary To The Nearest Thousandth Express 0 Between T And T class=

Sagot :

To answer this question we will use the following formula for the angle corresponding to a complex number z:

[tex]\theta=\arctan (\frac{\operatorname{Im}(z)}{\operatorname{Re}(z)})\text{.}[/tex]

In this case:

[tex]\begin{gathered} \operatorname{Re}(z)=8, \\ \operatorname{Im}(z)=-9. \end{gathered}[/tex]

Therefore:

[tex]\theta=\arctan (\frac{-9}{8})\approx-0.844.[/tex]

Answer:

[tex]\theta=-0.844.[/tex]

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