Chapter 9: Q. 7 (page 591)

Let $Z_{1} = r_{1} (\cos θ_{1} + i \sin θ_{1})$ and $Z_{2} = r_{2} (\cos θ_{2} + i \sin θ_{2})$
be two complex numbers. Then
$Z_{1} Z_{2} =__[\cos (_) + i \sin (____)]$

Short Answer

Expert verified

$Z_{1} Z_{2} = r_{1} r_{2} [\cos (θ_{1} + θ_{2}) + i \sin (θ_{1} + θ_{2})]$

Step by step solution

Step 1. Given

Given complex number in polar form

$z = r \cos θ + i \sin θ$

Calculation

$Z_{1} Z_{2} = r_{1} (\cos θ_{1} + i \sin θ_{1}) \times r_{2} (\cos θ_{2} + i \sin θ_{2}) = r_{1} r_{2} (\cos θ_{1} \cos θ_{2} + i \cos θ_{1} \sin θ_{2} + i \sin θ_{1} \cos θ_{2} + i^{2} \sin θ_{1} \sin θ_{2}) = r_{1} r_{2} [(\cos (θ_{1} + θ_{2}) + i \sin (θ_{1} + θ_{2})]$

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Let $Z_{1} = r_{1} (\cos θ_{1} + i \sin θ_{1})$ and $Z_{2} = r_{2} (\cos θ_{2} + i \sin θ_{2})$
be two complex numbers. Then
$Z_{1} Z_{2} =__[\cos (_) + i \sin (____)]$

Short Answer

Step by step solution

Step 1. Given

Calculation

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Let Z1=r1(cosθ1+isinθ1)and Z2=r2(cosθ2+isinθ2)be two complex numbers. ThenZ1Z2=____[cos(___)+isin(____)]

Short Answer

Step by step solution

Step 1. Given

Calculation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

Geometry

Decision Maths

Mechanics Maths

Applied Mathematics

Probability and Statistics

Study anywhere. Anytime. Across all devices.

Let $Z_{1} = r_{1} (\cos θ_{1} + i \sin θ_{1})$ and $Z_{2} = r_{2} (\cos θ_{2} + i \sin θ_{2})$
be two complex numbers. Then
$Z_{1} Z_{2} =__[\cos (_) + i \sin (____)]$