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प्रश्न
Answer the following:
Find the modulus and argument of a complex number and express it in the polar form.
6 − i
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उत्तर
Let z = 6 − i
∴ a = 6, b = − 1, a > 0, b < 0
∴ |z| = r
= `sqrt("a"^2 + "b"^2)`
= `sqrt(6^2 + (-1)^2)`
= `sqrt(36 + 1)`
= `sqrt(37)`
Here (6, −1) lies in 4th quadrant
∴ amp (z) = θ = `2pi + tan^-1 ("b"/"a")`
= `2pi + tan^-1 ((-1)/6)`
∴ the polar form of z = r(cos θ + i sin θ)
= `sqrt(37)(cos theta + "i" sin theta)`
where θ = `2pi + tan^-1 (-1/6)`
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