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Determine the absolute value and the argument value of the following number. (a)...

Question:

Determine the absolute value and the argument value of the following number.

(a) {eq}z_1=\frac{(3-3i)^4(-4 + 3i)^3}{(-1-i)^3(4i)^4} {/eq}

2. Find the absolute value of {eq}z_2 =\frac{1000(3 -3i)^4(-4+3 i)^3}{(-6-8i)^3(10i)^3} {/eq}

3. Compute {eq}e^z {/eq} in the form {eq}x + iy {/eq} and {eq}|e^z| {/eq} where z equals

(a) {eq}3 + \pi i {/eq}

(b) 1 + i

(c) {eq}\frac{3}{4}\pi i {/eq}

Polar Form:

The Polar form of a complex number {eq}z{/eq} where {eq}z=x+iy{/eq} is defined by {eq}z={{e}^{i\theta }}{/eq} where {eq}i=\sqrt{-1}{/eq} and {eq}\theta{/eq} is the angle between real part and imaginary part of a complex number defined by {eq}\theta ={{\tan }^{-1}}\left( \dfrac{y}{x} \right){/eq} and given by the expression {eq}z=\cos \theta +i\left( sin\theta \right){/eq}

Answer and Explanation:

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1.

Given complex number is {eq}{{z}_{1}}=\dfrac{{{\left( 3-3i \right)}^{4}}{{\left( -4+3i \right)}^{3}}}{{{\left( -1-i \right)}^{3}}{{\left( 4i...

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Complex Numbers in Polar Form: Process & Examples

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Chapter 24 / Lesson 2
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After watching this video lesson, you will be able to convert complex numbers from rectangular form to polar form easily by following the formulas you will see here. You will also learn how to find the power of a complex number.


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