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प्रश्न
Answer the following:
Find the modulus and argument of a complex number and express it in the polar form.
2i
उत्तर
Let z = 2i = 0 + 2i
∴ a = 0, b = 2
∴ z lies on positive imaginary Y-axis
∴ |z| = r
= `sqrt("a"^2 + "b"^2)`
= `sqrt(0^2 + 2^2)`
= `sqrt(0 + 4)`
= 2
∴ amp (z) = θ = `pi/2`
∴ θ = 90° = `pi/2`
∴ the polar form of z = r(cos θ + i sin θ)
= 2(cos 90° + i sin 90°)
= `2(cos pi/2 + "i" sin pi/2)`
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