Convert to Trigonometric Form |-7-9i|

Problem

|−7−9*i|

Solution

1. Identify the complex number z inside the absolute value bars as z=−7−9*i where the real part is a=−7 and the imaginary part is b=−9

2. Recall that the absolute value (or modulus) of a complex number z=a+b*i is defined as |z|=√(,a2+b2)

3. Substitute the values of a and b into the modulus formula.

|−7−9*i|=√(,(−7)2+(−9)2)

4. Square the components and sum them.

|−7−9*i|=√(,49+81)

5. Simplify the expression under the radical.

|−7−9*i|=√(,130)

6. Determine the trigonometric form of a constant real number. Since √(,130) is a positive real number, its representation in trigonometric form r*(cos(θ)+i*sin(θ)) uses r=√(,130) and θ=0

Final Answer

|−7−9*i|=√(,130)*(cos(0)+i*sin(0))

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