How do you write the trigonometric form of $- 2 i$ $-2i$ ?

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Answer 1 · 2018-04-17T06:10:15

Please read the explanation.

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Given the Complex Number: $- 2 i$ $color(blue)(-2i$

The standard form of a complex number is $z = a + b i$ $color(red)(z = a+bi$

So, we have $z = - 2 i = 0 - 2 i$ $z=-2i = 0-2i$ with $a = 0 and b = - 2$ $a=0 and b=-2$

The complex number $- 2 i$ $color(blue)(-2i$ is marked on a Complex Plane

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Observe that $- 2 i$ $color(blue)(-2i$ lies on the imaginary axis and it takes the same position as $A = (0, - 2)$ $A=(0,-2)$ in Quadrant-3.

This point makes a $270^{\circ}$ $color(red)(270^@)$ from the Real Axis measured in the counter-clockwise direction.

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$270^{\circ} = \frac{3 π}{2}$ $color(red)(270^@)=(3pi)/2$ Radians.

Using the formula,

$z = r (cos θ + i sin θ)$ $color(red)(z=r(cos theta + i sin theta)$

$r$ $r$ is the Modulus of z, $| z | = | a + b i | = \sqrt{a^{2} + b^{2}}$ $color(red)(|z|=|a+bi|=sqrt(a^2+b^2$

$θ$ $theta$ is the argument.

we can represent the complex number $Z = 0 - 2 i$ $Z=0-2i$ in trigonometric form as follows:

$r$ $r$ is the radius, which is $2$ $2$ in this problem.

Hence,

$z = 2 [cos (\frac{3 π}{2}) + i sin (\frac{3 π}{2})]$ $z=2[cos((3pi)/2)+i sin ((3pi)/2)]$

Hope it helps.

How do you write the trigonometric form of −2i-2i?