Express the complex number in trigonometric form. 6 - 6i

Solution:

6 - 6i is of the form a + bi

To express a + bi in trignometric form we apply the following expressions:

r = IzI = radius = √(a² + b²)

a = rcos(θ)

b = rsin(θ)

Therefore 

r = √(6)² + (-6)² = √(36 + 36) = √72 = √(2 × 36) = 6√2

Tan(θ) = b/a = -6/6 = -1

Therefore θ can be

(π-π/4) or (2π - π/4) because tan function is negative in the 2nd and 4th quadrant.

Hence the trigonometric forms of the equation are

(1) 6√2cos(3π/4) + i6√2sin(3π/4) or 

(2) 6√2cos(7π/4) + i6√2sin(7π/4)

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Express the complex number in trigonometric form. 6 - 6i

Summary:

6 - 6i can be expressed in the trigonometric form as 6√2Cos(3π/4) + i6√2Sin(3π/4) or 6√2Cos(7π/4) + i6√2Sin(7π/4)