Show that for complex numbers z1 = r1(cosθ1 + isinθ1) and z2 = r2(cosθ2 + isinθ2), their product z1z2 = r1r2[cos(θ1 + θ2) + i sin(θ1 + θ2)].

April 22, 2026Mathematics

ScanSolve AI Answer

April 22, 2026

Answer

$[r_1(\cos\theta_1 + i\sin\theta_1)][r_2(\cos\theta_$

Here's the solution to the questions from the image.

3b) Given the complex numbers $z_1 = r_1(\cos\theta_1 + i\sin\theta_1)$ and $z_2 = r_2(\cos\theta_2 + i\sin\theta_2)$ , show that $z_1z_2 = r_1r_2[\cos(\theta_1 + \theta_2) + i\sin(\theta_1 + \theta_2)]$ .

Step 1: Write the product $z_1z_2$ .

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Here's the solution to the questions from the image. 3b) Given the complex numbers z_1 = r_1(_1 + i_1) and z_2 = r_2(_2 + i_2), show that z_1z_2 = r_1r_2[(_1 + _2) + i(_1 + _2)].

Asked on April 22, 2026Mathematics

This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.

ScanSolve AI AnswerAnswered on April 22, 2026

Here's the solution to the questions from the image. 3b) Given the complex numbers z_1 = r_1(_1 + i_1) and z_2 = r_2(_2 + i_2), show that z_1z_2 = r_1r_2[(_1 + _2) + i(_1 + _2)]. Step 1: Write the product z_1z_2. z_1z_2 = [r_1(_1 + i_1)][r_2(_